Log in

Relevant bibliographies by topics / Groupoid Representations / Journal articles

To see the other types of publications on this topic, follow the link: Groupoid Representations.

Journal articles on the topic 'Groupoid Representations'

Author: Grafiati

Published: 4 June 2025

Last updated: 15 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Groupoid Representations.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Ibort, Alberto, and Miguel Rodríguez. "On the Structure of Finite Groupoids and Their Representations." Symmetry 11, no. 3 (2019): 414. http://dx.doi.org/10.3390/sym11030414.

Full text

Abstract:

In this paper, both the structure and the theory of representations of finite groupoids are discussed. A finite connected groupoid turns out to be an extension of the groupoids of pairs of its set of units by its canonical totally disconnected isotropy subgroupoid. An extension of Maschke’s theorem for groups is proved showing that the algebra of a finite groupoid is semisimple and all finite-dimensional linear representations of finite groupoids are completely reducible. The theory of characters for finite-dimensional representations of finite groupoids is developed and it is shown that irreducible representations of the groupoid are in one-to-one correspondence with irreducible representation of its isotropy groups, with an extension of Burnside’s theorem describing the decomposition of the regular representation of a finite groupoid. Some simple examples illustrating these results are exhibited with emphasis on the groupoids interpretation of Schwinger’s description of quantum mechanical systems.

APA, Harvard, Vancouver, ISO, and other styles

2

Giżycki, Artur, and Leszek Pysiak. "Multiplicity formulas for representations of transformation groupoids." Demonstratio Mathematica 50, no. 1 (2017): 42–50. http://dx.doi.org/10.1515/dema-2017-0004.

Full text

Abstract:

Abstract We study the representations of transitive transformation groupoids with the aim of generalizing the Mackey theory. Using the Mackey theory and a bijective correspondence between the imprimitivity systems and the representations of a transformation groupoid we derive the irreducibility theory. Then we derive the direct sum decomposition for representations of a groupoid together with the formula for the multiplicity of subrepresentations. We discuss a physical interpretation of this formula. Finally, we prove the claim analogous to the Peter-Weyl theorem for a noncompact transformation groupoid. We show that the representation theory of a transitive transformation groupoids is closely related to the representation theory of a compact groups.

APA, Harvard, Vancouver, ISO, and other styles

3

Matsnev, Dmitry, and Pedro Resende. "Étale groupoids as germ groupoids and their base extensions." Proceedings of the Edinburgh Mathematical Society 53, no. 3 (2010): 765–85. http://dx.doi.org/10.1017/s001309150800076x.

Full text

Abstract:

AbstractWe introduce the notion of wide representation of an inverse semigroup and prove that with a suitably defined topology there is a space of germs of such a representation that has the structure of an étale groupoid. This gives an elegant description of Paterson's universal groupoid and of the translation groupoid of Skandalis, Tu and Yu. In addition, we characterize the inverse semigroups that arise from groupoids, leading to a precise bijection between the class of étale groupoids and the class of complete and infinitely distributive inverse monoids equipped with suitable representations, and we explain the sense in which quantales and localic groupoids carry a generalization of this correspondence.

APA, Harvard, Vancouver, ISO, and other styles

4

Muhly, Paul S., and Baruch Solel. "Representations of triangular subalgebras of groupoid C*-algebras." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 61, no. 3 (1996): 289–321. http://dx.doi.org/10.1017/s1446788700000392.

Full text

Abstract:

AbstractWe investigate the invariant subspace structure of subalgebras of groupoid C*-algebras that are determined by automorphism groups implemented by cocycles on the groupoids. The invariant subspace structure is intimately tied to the asymptotic behavior of the cocycle.

APA, Harvard, Vancouver, ISO, and other styles

5

Esposito, Chiara, Luca Vitagliano, and Alfonso Giuseppe Tortorella. "Infinitesimal Automorphisms of VB-Groupoids and Algebroids." Quarterly Journal of Mathematics 70, no. 3 (2019): 1039–89. http://dx.doi.org/10.1093/qmath/haz007.

Full text

Abstract:

Abstract VB-groupoids and algebroids are vector bundle objects in the categories of Lie groupoids and Lie algebroids, respectively, and they are related via the Lie functor. VB-groupoids and algebroids play a prominent role in Poisson and related geometries. Additionally, they can be seen as models for vector bundles over singular spaces. In this paper we study their infinitesimal automorphisms, i.e. vector fields on them generating a flow by diffeomorphisms preserving both the linear and the groupoid/algebroid structures. For a special class of VB-groupoids/algebroids coming from representations of Lie groupoids/algebroids, we prove that infinitesimal automorphisms are the same as multiplicative sections of a certain derivation VB-groupoid/algebroid.

APA, Harvard, Vancouver, ISO, and other styles

6

Mantoiu, Marius. "C∗-Algebraic spectral sets, twisted groupoids and operators." Journal of Operator Theory 86, no. 2 (2021): 355–94. http://dx.doi.org/10.7900/jot.2020may05.2272.

Full text

Abstract:

We treat spectral problems by twisted groupoid methods. To Hausdorff locally compact groupoids endowed with a continuous 2-cocycle one associates the reduced twisted groupoid C∗-algebra. Elements (or multipliers) of this algebra admit natural Hilbert space representations. We show the relevance of the orbit closure structure of the unit space of the groupoid in dealing with spectra, norms, numerical ranges and ε-pseudospectra of the resulting operators. As an example, we treat a class of pseudo-differential operators introduced recently, associated to group actions. We also prove a decomposition principle for bounded operators connected to groupoids, showing that several relevant spectral quantities of these operators coincide with those of certain non-invariant restrictions. This is applied to Toeplitz-like operators with variable coefficients and to band dominated operators on discrete metric spaces.

APA, Harvard, Vancouver, ISO, and other styles

7

Gabriel, Bittencourt Rios, and Luiz Mariano Hugo. "Model Theory Inspired by Grothendieckian Algebraic Geometry: a Survey of Sheaf Representations for Categorical Model Theory." Latin American Journal of Mathematics 02, no. 01 (2023): 12–50. https://doi.org/10.5281/zenodo.7926048.

Full text

Abstract:

In this survey, we expound sheaf representations of categories in the context of categorical logic. Namely, we present classifying topoi of coherent theories in terms of equivariant sheaves over a topological groupoid, show a generalization of this technique using localic groupoids and finally expose a representation of Grothendieck topoi as global sections of sheaf. Finally, we apply these techniques to provide a quick glance at logical schemes, a novel theory proposed as the model-theoretic analogue to the schemes of Algebraic Geometry.

APA, Harvard, Vancouver, ISO, and other styles

8

Amini, Massoud, and Alireza Medghalchi. "Restricted Algebras on Inverse Semigroups—Part II: Positive Definite Functions." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–21. http://dx.doi.org/10.1155/2011/324821.

Full text

Abstract:

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. In this paper, we investigate the concept of restricted positive definite functions and their relation with restricted representations of an inverse semigroup. We also introduce the restricted Fourier and Fourier-Stieltjes algebras of an inverse semigroup and study their relation with the corresponding algebras on the associated groupoid.

APA, Harvard, Vancouver, ISO, and other styles

9

LAWSON, M. V., S. W. MARGOLIS, and B. STEINBERG. "THE ÉTALE GROUPOID OF AN INVERSE SEMIGROUP AS A GROUPOID OF FILTERS." Journal of the Australian Mathematical Society 94, no. 2 (2013): 234–56. http://dx.doi.org/10.1017/s144678871200050x.

Full text

Abstract:

AbstractPaterson showed how to construct an étale groupoid from an inverse semigroup using ideas from functional analysis. This construction was later simplified by Lenz. We show that Lenz’s construction can itself be further simplified by using filters: the topological groupoid associated with an inverse semigroup is precisely a groupoid of filters. In addition, idempotent filters are closed inverse subsemigroups and so determine transitive representations by means of partial bijections. This connection between filters and representations by partial bijections is exploited to show how linear representations of inverse semigroups can be constructed from the groups occurring in the associated topological groupoid.

APA, Harvard, Vancouver, ISO, and other styles

10

Choudhury, Vikraman, Jacek Karwowski, and Amr Sabry. "Symmetries in reversible programming: from symmetric rig groupoids to reversible programming languages." Proceedings of the ACM on Programming Languages 6, POPL (2022): 1–32. http://dx.doi.org/10.1145/3498667.

Full text

Abstract:

The Pi family of reversible programming languages for boolean circuits is presented as a syntax of combinators witnessing type isomorphisms of algebraic data types. In this paper, we give a denotational semantics for this language, using weak groupoids à la Homotopy Type Theory, and show how to derive an equational theory for it, presented by 2-combinators witnessing equivalences of type isomorphisms. We establish a correspondence between the syntactic groupoid of the language and a formally presented univalent subuniverse of finite types. The correspondence relates 1-combinators to 1-paths, and 2-combinators to 2-paths in the universe, which is shown to be sound and complete for both levels, forming an equivalence of groupoids. We use this to establish a Curry-Howard-Lambek correspondence between Reversible Logic, Reversible Programming Languages, and Symmetric Rig Groupoids, by showing that the syntax of Pi is presented by the free symmetric rig groupoid, given by finite sets and bijections. Using the formalisation of our results, we perform normalisation-by-evaluation, verification and synthesis of reversible logic gates, motivated by examples from quantum computing. We also show how to reason about and transfer theorems between different representations of reversible circuits.

APA, Harvard, Vancouver, ISO, and other styles

11

WALDMANN, STEFAN. "STATES AND REPRESENTATIONS IN DEFORMATION QUANTIZATION." Reviews in Mathematical Physics 17, no. 01 (2005): 15–75. http://dx.doi.org/10.1142/s0129055x05002297.

Full text

Abstract:

In this review we discuss various aspects of representation theory in deformation quantization starting with a detailed introduction to the concepts of states as positive functionals and the GNS construction. Rieffel induction of representations as well as strong Morita equivalence, Dirac monopole and strong Picard Groupoid are also discussed.

APA, Harvard, Vancouver, ISO, and other styles

12

Constantinescu, F., and F. Toppan. "On the Linearized Artin Braid Representation." Journal of Knot Theory and Its Ramifications 02, no. 04 (1993): 399–412. http://dx.doi.org/10.1142/s0218216593000222.

Full text

Abstract:

We linearize the Artin representation of the braid group given by (right) automorphisms of a free group providing a linear faithful representation of the braid group. This result is generalized to obtain linear representations for the coloured braid groupoid and pure braid group too. Applications to some areas of two-dimensional physics are mentioned.

APA, Harvard, Vancouver, ISO, and other styles

13

Ionescu, Marius, and Dana P. Williams. "Irreducible representations of groupoid $C^*$-algebras." Proceedings of the American Mathematical Society 137, no. 04 (2008): 1323–32. http://dx.doi.org/10.1090/s0002-9939-08-09782-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Sheng, Yunhe, and Chenchang Zhu. "Higher extensions of Lie algebroids." Communications in Contemporary Mathematics 19, no. 03 (2017): 1650034. http://dx.doi.org/10.1142/s0219199716500346.

Full text

Abstract:

We study the extension of a Lie algebroid by a representation up to homotopy, including semidirect products of a Lie algebroid with such representations. The extension results in a higher Lie algebroid. We give exact Courant algebroids and string Lie 2-algebras as examples of such extensions. We then apply this to obtain a Lie 2-groupoid integrating an exact Courant algebroid.

APA, Harvard, Vancouver, ISO, and other styles

15

Amiri, Habib, and Alexander Schmeding. "Linking Lie groupoid representations and representations of infinite-dimensional Lie groups." Annals of Global Analysis and Geometry 55, no. 4 (2019): 749–75. http://dx.doi.org/10.1007/s10455-019-09650-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Bittencourt Rios, Gabriel, and Hugo Luiz Mariano. "Model Theory Inspired by Modern Algebraic Geometry." Latin American Journal of Mathematics 2, no. 01 (2023): 12–50. http://dx.doi.org/10.14244/lajm.v2i01.8.

Full text

Abstract:

In this survey, we expound sheaf representations of categories in the context of categorical logic. Namely, we present classifying topoi of coherent theories in terms of equivariant sheaves of groupoid (and then explore the generalization of this technique to a more general categorical context); expose a representation of Grothendieck topoi as global sections of sheaf and, finally, show a quick introduction to logical schemes, a proposed model-theoretic analogue to the schemes of Algebraic Geometry.

APA, Harvard, Vancouver, ISO, and other styles

17

Amini, Massoud, Alireza Medghalchi, and Ahmad Shirinkalam. "1-Algebra of a Locally Compact Groupoid." ISRN Algebra 2011 (June 29, 2011): 1–17. http://dx.doi.org/10.5402/2011/856709.

Full text

Abstract:

For a locally compact groupoid with a fixed Haar system and quasi-invariant measure , we introduce the notion of -measurability and construct the space 1(, , ) of absolutely integrable functions on and show that it is a Banach -algebra and a two-sided ideal in the algebra () of complex Radon measures on . We find correspondences between representations of on Hilbert bundles and certain class of nondegenerate representations of 1(, , ).

APA, Harvard, Vancouver, ISO, and other styles

18

Dudko, Artem, and Rostislav Grigorchuk. "On spectra of Koopman, groupoid and quasi-regular representations." Journal of Modern Dynamics 11, no. 1 (2017): 99–123. http://dx.doi.org/10.3934/jmd.2017005.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Andersen, Jørgen Ellegaard, Alex James Bene, and R. C. Penner. "Groupoid extensions of mapping class representations for bordered surfaces." Topology and its Applications 156, no. 17 (2009): 2713–25. http://dx.doi.org/10.1016/j.topol.2009.08.001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Carvalho, Catarina, Victor Nistor, and Yu Qiao. "Fredholm criteria for pseudodifferential operators and induced representations of groupoid algebras." Electronic Research Announcements in Mathematical Sciences 24 (August 2017): 68–77. http://dx.doi.org/10.3934/era.2017.24.008.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Chang, Wonjun, Byung Chun Kim, and Yongjin Song. "An infinite family of braid group representations in automorphism groups of free groups." Journal of Knot Theory and Its Ramifications 29, no. 10 (2020): 2042007. http://dx.doi.org/10.1142/s0218216520420079.

Full text

Abstract:

The [Formula: see text]-fold ([Formula: see text]) branched coverings on a disk give an infinite family of nongeometric embeddings of braid groups into mapping class groups. We, in this paper, give new explicit expressions of these braid group representations into automorphism groups of free groups in terms of the actions on the generators of free groups. We also give a systematic way of constructing and expressing these braid group representations in terms of a new gadget, called covering groupoid. We prove that each generator [Formula: see text] of braid group inside mapping class group induced by [Formula: see text]-fold covering is the product of [Formula: see text] Dehn twists on the surface.

APA, Harvard, Vancouver, ISO, and other styles

22

Kubota, Yosuke. "Notes on twisted equivariant K-theory for C*-algebras." International Journal of Mathematics 27, no. 06 (2016): 1650058. http://dx.doi.org/10.1142/s0129167x16500580.

Full text

Abstract:

In this paper, we study a generalization of twisted (groupoid) equivariant K-theory in the sense of Freed–Moore for [Formula: see text]-graded [Formula: see text]-algebras. It is defined by using Fredholm operators on Hilbert modules with twisted representations. We compare it with another description using odd symmetries, which is a generalization of van Daele’s K-theory for [Formula: see text]-graded Banach algebras. In particular, we obtain a simple presentation of the twisted equivariant K-group when the [Formula: see text]-algebra is trivially graded. It is applied for the bulk-edge correspondence of topological insulators with CT-type symmetries.

APA, Harvard, Vancouver, ISO, and other styles

23

Caenepeel, S., and T. Fieremans. "Descent and Galois theory for Hopf categories." Journal of Algebra and Its Applications 17, no. 07 (2018): 1850120. http://dx.doi.org/10.1142/s0219498818501207.

Full text

Abstract:

Descent theory for linear categories is developed. Given a linear category as an extension of a diagonal category, we introduce descent data, and the category of descent data is isomorphic to the category of representations of the diagonal category, if some flatness assumptions are satisfied. Then Hopf–Galois descent theory for linear Hopf categories, the Hopf algebra version of a linear category, is developed. This leads to the notion of Hopf–Galois category extension. We have a dual theory, where actions by dual linear Hopf categories on linear categories are considered. Hopf–Galois category extensions over groupoid algebras correspond to strongly graded linear categories.

APA, Harvard, Vancouver, ISO, and other styles

24

Carolina, Sparavigna Amelia. "Some Groupoids and their Representations by Means of Integer Sequences." International Journal of Sciences Volume 8, no. 2019-10 (2019): 1–5. https://doi.org/10.5281/zenodo.3979993.

Full text

Abstract:

In some previous works, we have discussed the groupoids related to the integer sequences of Mersenne, Fermat, Cullen, Woodall and other numbers. These groupoids possess different binary operators. As we can easily see, other integer sequences can have the same binary operators, and therefore can be used to represent the related groupoids. Using the On-Line Encyclopedia of Integer Sequences (OEIS), we are able to identify the properties of these representations of groupoids. At the same time, we can also find integer sequences not given in OEIS and probably not yet studied.Read Complete Article at ijSciences: V82019102188 AND DOI: http://dx.doi.org/10.18483/ijSci.2188

APA, Harvard, Vancouver, ISO, and other styles

25

Sparavigna, Amelia Carolina. "Some Groupoids and their Representations by Means of Integer Sequences." International Journal of Sciences 8, no. 10 (2019): 1–5. https://doi.org/10.18483/ijSci.2188.

Full text

Abstract:

In some previous works, we have discussed the groupoids related to the integer sequences of Mersenne, Fermat, Cullen, Woodall and other numbers. These groupoids possess different binary operators. As we can easily see, other integer sequences can have the same binary operators, and therefore can be used to represent the related groupoids. Using the On-Line Encyclopedia of Integer Sequences (OEIS), we are able to identify the properties of these representations of groupoids. At the same time, we can also find integer sequences not given in OEIS and probably not yet studied.

APA, Harvard, Vancouver, ISO, and other styles

26

Ehsani, Amir, and Yuri Movsisyan. "A REPRESENTATION OF PARAMEDIAL n-ARY GROUPOIDS." Asian-European Journal of Mathematics 07, no. 01 (2014): 1450020. http://dx.doi.org/10.1142/s179355711450020x.

Full text

Abstract:

In this paper, we prove that paramedial n-ary groupoid with an idempotent regular element has a linear representation. Also, we obtain a linear representation for paramedial n-ary groupoids without an idempotent element. As a consequence of the above results, we obtain the linear representation for paramedial n-ary quasigroups.

APA, Harvard, Vancouver, ISO, and other styles

27

di Cosmo, F., A. Ibort, and G. Marmo. "Groupoids and Coherent States." Open Systems & Information Dynamics 26, no. 04 (2019): 1950017. http://dx.doi.org/10.1142/s1230161219500173.

Full text

Abstract:

Schwinger’s algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids. Thus given a quantum mechanical system with associated Hilbert space determined by a representation of a groupoid, it is shown that any invariant subset of the group of invertible elements in the groupoid algebra determines a family of generalized coherent states provided that a completeness condition is satisfied. The standard coherent states for the harmonic oscillator as well as generalized coherent states for f-oscillators are exemplified in this picture.

APA, Harvard, Vancouver, ISO, and other styles

28

CLARK, LISA ORLOFF, and ASTRID AN HUEF. "The representation theory of C*-algebras associated to groupoids." Mathematical Proceedings of the Cambridge Philosophical Society 153, no. 1 (2012): 167–91. http://dx.doi.org/10.1017/s0305004112000047.

Full text

Abstract:

AbstractLet E be a second-countable, locally compact, Hausdorff groupoid equipped with an action of such that G: = E/ is a principal groupoid with Haar system λ. The twisted groupoid C*-algebra C*(E; G, λ) is a quotient of the C*-algebra of E obtained by completing the space of -equivariant functions on E. We show that C*(E; G, λ) is postliminal if and only if the orbit space of G is T0 and that C*(E; G, λ) is liminal if and only if the orbit space is T1. We also show that C*(E; G, λ) has bounded trace if and only if G is integrable and that C*(E; G, λ) is a Fell algebra if and only if G is Cartan.Let be a second-countable, locally compact, Hausdorff groupoid with Haar system λ and continuously varying, abelian isotropy groups. Let be the isotropy groupoid and : = /. Using the results about twisted groupoid C*-algebras, we show that the C*-algebra C*(, λ) has bounded trace if and only if is integrable and that C*(, λ) is a Fell algebra if and only if is Cartan. We illustrate our theorems with examples of groupoids associated to directed graphs.

APA, Harvard, Vancouver, ISO, and other styles

29

Crainic, Marius, João Nuno Mestre, and Ivan Struchiner. "Deformations of Lie Groupoids." International Mathematics Research Notices 2020, no. 21 (2018): 7662–746. http://dx.doi.org/10.1093/imrn/rny221.

Full text

Abstract:

Abstract We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several fundamental properties of the deformation cohomology including Morita invariance, a van Est theorem, and a vanishing result in the proper case. Combined with Moser’s deformation arguments for groupoids, we obtain several rigidity and normal form results.

APA, Harvard, Vancouver, ISO, and other styles

30

Ciaglia, F. M., F. Di Cosmo, A. Ibort, G. Marmo, L. Schiavone, and A. Zampini. "Feynman’s propagator in Schwinger’s picture of Quantum Mechanics." Modern Physics Letters A 36, no. 26 (2021): 2150187. http://dx.doi.org/10.1142/s021773232150187x.

Full text

Abstract:

A novel derivation of Feynman’s sum-over-histories construction of the quantum propagator using the groupoidal description of Schwinger picture of Quantum Mechanics is presented. It is shown that such construction corresponds to the GNS representation of a natural family of states called Dirac–Feynman–Schwinger (DFS) states. Such states are obtained from a q-Lagrangian function [Formula: see text] on the groupoid of configurations of the system. The groupoid of histories of the system is constructed and the q-Lagrangian [Formula: see text] allows us to define a DFS state on the algebra of the groupoid. The particular instance of the groupoid of pairs of a Riemannian manifold serves to illustrate Feynman’s original derivation of the propagator for a point particle described by a classical Lagrangian L.

APA, Harvard, Vancouver, ISO, and other styles

31

Clark, Lisa O., Benjamin Steinberg, and Daniel W. van Wyk. "GCR and CCR Steinberg Algebras." Canadian Journal of Mathematics 72, no. 6 (2019): 1581–606. http://dx.doi.org/10.4153/s0008414x19000415.

Full text

Abstract:

AbstractKaplansky introduced the notions of CCR and GCR $C^{\ast }$-algebras, because they have a tractable representation theory. Many years later, he introduced the notions of CCR and GCR rings. In this paper we characterize when the algebra of an ample groupoid over a field is CCR and GCR. The results turn out to be exact analogues of the corresponding characterization of locally compact groupoids with CCR and GCR $C^{\ast }$-algebras. As a consequence, we classify the CCR and GCR Leavitt path algebras.

APA, Harvard, Vancouver, ISO, and other styles

32

Zelinka, Bohdan. "Representation of undirected graphs by anticommutative conservative groupoids." Mathematica Bohemica 119, no. 3 (1994): 231–37. http://dx.doi.org/10.21136/mb.1994.126168.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Palmigiano, Alessandra, and Riccardo Re. "Relational Representation of Groupoid Quantales." Order 30, no. 1 (2011): 65–83. http://dx.doi.org/10.1007/s11083-011-9227-z.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Kališnik, J. "Representations of orbifold groupoids." Topology and its Applications 155, no. 11 (2008): 1175–88. http://dx.doi.org/10.1016/j.topol.2008.02.004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Romanowska, A., and B. Roszkowska. "Representations ofn-cyclic groupoids." Algebra Universalis 26, no. 1 (1989): 7–15. http://dx.doi.org/10.1007/bf01243869.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Ciccoli, Nicola. "Quantum Orbit Method in the Presence of Symmetries." Symmetry 13, no. 4 (2021): 724. http://dx.doi.org/10.3390/sym13040724.

Full text

Abstract:

We review some of the main achievements of the orbit method, when applied to Poisson–Lie groups and Poisson homogeneous spaces or spaces with an invariant Poisson structure. We consider C∗-algebra quantization obtained through groupoid techniques, and we try to put the results obtained in algebraic or representation theoretical contexts in relation with groupoid quantization.

APA, Harvard, Vancouver, ISO, and other styles

37

Kohno, Toshitake. "Higher holonomy of formal homology connections and braid cobordisms." Journal of Knot Theory and Its Ramifications 25, no. 12 (2016): 1642007. http://dx.doi.org/10.1142/s0218216516420074.

Full text

Abstract:

We construct a representation of the homotopy 2-groupoid of a manifold by means of Chen’s formal homology connections. By using the idea of this 2-holonomy map, we describe a method to obtain a representation of the category of braid cobordisms.

APA, Harvard, Vancouver, ISO, and other styles

38

Gracia-Saz, Alfonso, and Rajan Amit Mehta. "$\mathcal{VB}$-groupoids and representation theory of Lie groupoids." Journal of Symplectic Geometry 15, no. 3 (2017): 741–83. http://dx.doi.org/10.4310/jsg.2017.v15.n3.a5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Amiri, H., and M. Lashkarizadeh Bami. "Square Integrable Representation of Groupoids." Acta Mathematica Sinica, English Series 23, no. 2 (2006): 327–40. http://dx.doi.org/10.1007/s10114-005-0814-z.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Trentinaglia, Giorgio. "Regular Cartan groupoids and longitudinal representations." Advances in Mathematics 340 (December 2018): 1–47. http://dx.doi.org/10.1016/j.aim.2018.10.006.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Evans, Trevor. "Embedding and representation theorems for clones and varieties." Bulletin of the Australian Mathematical Society 40, no. 2 (1989): 199–205. http://dx.doi.org/10.1017/s0004972700004305.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

del Hoyo, Matias, and Cristian Ortiz. "Morita Equivalences of Vector Bundles." International Mathematics Research Notices 2020, no. 14 (2018): 4395–432. http://dx.doi.org/10.1093/imrn/rny149.

Full text

Abstract:

Abstract We study vector bundles over Lie groupoids, known as VB-groupoids, and their induced geometric objects over differentiable stacks. We establish a fundamental theorem that characterizes VB-Morita maps in terms of fiber and basic data, and use it to prove the Morita invariance of VB-cohomology, with implications to deformation cohomology of Lie groupoids and of classic geometries. We discuss applications of our theory to Poisson geometry, providing a new insight over Marsden–Weinstein reduction and the integration of Dirac structures. We conclude by proving that the derived category of VB-groupoids is a Morita invariant, which leads to a notion of VB-stacks, and solves (an instance of) an open question on representations up to homotopy.

APA, Harvard, Vancouver, ISO, and other styles

43

Gardella, Eusebio, and Martino Lupini. "Representations of étale groupoids on L-spaces." Advances in Mathematics 318 (October 2017): 233–78. http://dx.doi.org/10.1016/j.aim.2017.07.023.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Hanaki, Akihide, and Masayoshi Yoshikawa. "Thin coherent configurations and groupoids." Journal of Algebra and Its Applications 14, no. 01 (2014): 1450074. http://dx.doi.org/10.1142/s0219498814500741.

Full text

Abstract:

In this paper, we will investigate thin coherent configurations. We will show that thin coherent configurations are equivalent to finite connected groupoids. Also, we will investigate their representations.

APA, Harvard, Vancouver, ISO, and other styles

45

BOS, ROGIER. "GEOMETRIC QUANTIZATION OF HAMILTONIAN ACTIONS OF LIE ALGEBROIDS AND LIE GROUPOIDS." International Journal of Geometric Methods in Modern Physics 04, no. 03 (2007): 389–436. http://dx.doi.org/10.1142/s0219887807002077.

Full text

Abstract:

We construct Hermitian representations of Lie algebroids and associated unitary representations of Lie groupoids by a geometric quantization procedure. For this purpose, we introduce a new notion of Hamiltonian Lie algebroid actions. The first step of our procedure consists of the construction of a prequantization line bundle. Next, we discuss a version of Kähler quantization suitable for this setting. We proceed by defining a Marsden–Weinstein quotient for our setting and prove a "quantization commutes with reduction" theorem. We explain how our geometric quantization procedure relates to a possible orbit method for Lie groupoids. Our theory encompasses the geometric quantization of symplectic manifolds, Hamiltonian Lie algebra actions, actions of bundles of Lie groups, and foliations, as well as some general constructions from differential geometry.

APA, Harvard, Vancouver, ISO, and other styles

46

Ciaglia, F. M., A. Ibort, and G. Marmo. "Schwinger’s picture of quantum mechanics I: Groupoids." International Journal of Geometric Methods in Modern Physics 16, no. 08 (2019): 1950119. http://dx.doi.org/10.1142/s0219887819501196.

Full text

Abstract:

A new picture of Quantum Mechanics based on the theory of groupoids is presented. This picture provides the mathematical background for Schwinger’s algebra of selective measurements and helps to understand its scope and eventual applications. In this first paper, the kinematical background is described using elementary notions from category theory, in particular the notion of 2-groupoids as well as their representations. Some basic results are presented, and the relation with the standard Dirac–Schrödinger and Born–Jordan–Heisenberg pictures are succinctly discussed.

APA, Harvard, Vancouver, ISO, and other styles

47

Nazarov, Maxim N. "Finite Representation of Classes of Isomorphic Groupoids." Journal of Siberian Federal University. Mathematics & Physics 8, no. 3 (2015): 312–19. http://dx.doi.org/10.17516/1997-1397-2014-7-3-312-319.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Nazarov, Maxim N. "Finite Representation of Classes of Isomorphic Groupoids." Journal of Siberian Federal University. Mathematics & Physics 8, no. 3 (2015): 312–19. http://dx.doi.org/10.17516/1997-1397-2015-8-3-312-319.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

MUHLY, PAUL S., and BARUCH SOLEL. "DILATIONS AND COMMUTANT LIFTING FOR SUBALGEBRAS OF GROUPOID C*-ALGEBRAS." International Journal of Mathematics 05, no. 01 (1994): 87–123. http://dx.doi.org/10.1142/s0129167x9400005x.

Full text

Abstract:

Let B be a nuclear C*-algebra that has a diagonal subalgebra D in the sense of Kumjian and let A be a closed, not necessarily self-adjoint subalgebra of B that contains D such that A + A* is dense in B. We show that every contractive representation of A has an essentially unique minimal dilation to a C*-representation of B and that the commutant of the representation of A can be lifted to the commutant of the dilation without increasing norms.

APA, Harvard, Vancouver, ISO, and other styles

50

Roszkowska-Lech, Barbara. "A REPRESENTATION OF SYMMETRIC IDEMPOTENT AND ENTROPIC GROUPOIDS." Demonstratio Mathematica 32, no. 2 (1999): 247–62. http://dx.doi.org/10.1515/dema-1999-0203.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!