Log in

Relevant bibliographies by topics / Braided crossed module / Journal articles

To see the other types of publications on this topic, follow the link: Braided crossed module.

Journal articles on the topic 'Braided crossed module'

Author: Grafiati

Published: 9 March 2023

Last updated: 19 July 2025

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

Select a source type:

Consult the top 27 journal articles for your research on the topic 'Braided crossed module.'

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

Noohi, Behrang. "Group cohomology with coefficients in a crossed module." Journal of the Institute of Mathematics of Jussieu 10, no. 2 (2010): 359–404. http://dx.doi.org/10.1017/s1474748010000186.

Full text

Abstract:

AbstractWe compare three different ways of defining group cohomology with coefficients in a crossed module: (1) explicit approach via cocycles; (2) geometric approach via gerbes; (3) group theoretic approach via butterflies. We discuss the case where the crossed module is braided and the case where the braiding is symmetric. We prove the functoriality of the cohomologies with respect to weak morphisms of crossed modules and also prove the ‘long’ exact cohomology sequence associated to a short exact sequence of crossed modules and weak morphisms.

APA, Harvard, Vancouver, ISO, and other styles

2

Davydov, Alexei, and Dmitri Nikshych. "The Picard crossed module of a braided tensor category." Algebra & Number Theory 7, no. 6 (2013): 1365–403. http://dx.doi.org/10.2140/ant.2013.7.1365.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Shi, Gui-Qi, Xiao-Li Fang, and Blas Torrecillas. "Generalized Yetter–Drinfeld (quasi)modules and Yetter–Drinfeld–Long bi(quasi)modules for Hopf quasigroups." Journal of Algebra and Its Applications 18, no. 02 (2019): 1950034. http://dx.doi.org/10.1142/s0219498819500348.

Full text

Abstract:

As generalizations of Yetter–Drinfeld module over a Hopf quasigroup, we introduce the notions of Yetter–Drinfeld–Long bimodule and generalize the Yetter–Drinfeld module over a Hopf quasigroup in this paper, and show that the category of Yetter–Drinfeld–Long bimodules [Formula: see text] over Hopf quasigroups is braided, which generalizes the results in Alonso Álvarez et al. [Projections and Yetter–Drinfeld modules over Hopf (co)quasigroups, J. Algebra 443 (2015) 153–199]. We also prove that the category of [Formula: see text] having all the categories of generalized Yetter–Drinfeld modules [Formula: see text], [Formula: see text] as components is a crossed [Formula: see text]-category.

APA, Harvard, Vancouver, ISO, and other styles

4

Ma, Tianshui, Linlin Liu та Haiying Li. "A class of braided monoidal categories via quasitriangular Hopf π-crossed coproduct algebras". Journal of Algebra and Its Applications 14, № 02 (2014): 1550010. http://dx.doi.org/10.1142/s0219498815500103.

Full text

Abstract:

Let π be a group and (H = {Hα}α∈π, μ, η) a Hopf π-algebra. First, we introduce the concept of quasitriangular Hopf π-algebra, and then prove that the left H-π-module category [Formula: see text], where (H, R) is a quasitriangular Hopf π-algebra, is a braided monoidal category. Second, we give the construction of Hopf π-crossed coproduct algebra [Formula: see text]. At last, the necessary and sufficient conditions for [Formula: see text] to be a quasitriangular Hopf π-algebra are derived, and in this case, [Formula: see text] is a braided monoidal category.

APA, Harvard, Vancouver, ISO, and other styles

5

Yan, Dongdong, and Shuanhong Wang. "Drinfel’d construction for Hom–Hopf T-coalgebras." International Journal of Mathematics 31, no. 08 (2020): 2050058. http://dx.doi.org/10.1142/s0129167x20500585.

Full text

Abstract:

Let [Formula: see text] be a Hom–Hopf T-coalgebra over a group [Formula: see text] (i.e. a crossed Hom–Hopf [Formula: see text]-coalgebra). First, we introduce and study the left–right [Formula: see text]-Yetter–Drinfel’d category [Formula: see text] over [Formula: see text], with [Formula: see text], and construct a class of new braided T-categories. Then, we prove that a Yetter–Drinfel’d module category [Formula: see text] is a full subcategory of the center [Formula: see text] of the category of representations of [Formula: see text]. Next, we define the quasi-triangular structure of [Formula: see text] and show that the representation crossed category [Formula: see text] is quasi-braided. Finally, the Drinfel’d construction [Formula: see text] of [Formula: see text] is constructed, and an equivalent relation between [Formula: see text] and the representation of [Formula: see text] is given.

APA, Harvard, Vancouver, ISO, and other styles

6

Ma, Tianshui, and Huihui Zheng. "An extended form of Majid’s double biproduct." Journal of Algebra and Its Applications 16, no. 04 (2017): 1750061. http://dx.doi.org/10.1142/s021949881750061x.

Full text

Abstract:

Let [Formula: see text] be a bialgebra. Let [Formula: see text] be a linear map, where [Formula: see text] is a left [Formula: see text]-module algebra, and a coalgebra with a left [Formula: see text]-weak coaction. Let [Formula: see text] be a linear map, where [Formula: see text] is a right [Formula: see text]-module algebra, and a coalgebra with a right [Formula: see text]-weak coaction. In this paper, we extend the construction of two-sided smash coproduct to two-sided crossed coproduct [Formula: see text]. Then we derive the necessary and sufficient conditions for two-sided smash product algebra [Formula: see text] and [Formula: see text] to be a bialgebra, which generalizes the Majid’s double biproduct in [Double-bosonization of braided groups and the construction of [Formula: see text], Math. Proc. Camb. Philos. Soc. 125(1) (1999) 151–192] and the Wang–Wang–Yao’s crossed coproduct in [Hopf algebra structure over crossed coproducts, Southeast Asian Bull. Math. 24(1) (2000) 105–113].

APA, Harvard, Vancouver, ISO, and other styles

7

Iğde, Elif, and Koray Yılmaz. "Tensor Products and Crossed Differential Graded Lie Algebras in the Category of Crossed Complexes." Symmetry 15, no. 9 (2023): 1646. http://dx.doi.org/10.3390/sym15091646.

Full text

Abstract:

The study of algebraic structures endowed with the concept of symmetry is made possible by the link between Lie algebras and symmetric monoidal categories. This relationship between Lie algebras and symmetric monoidal categories is useful and has resulted in many areas, including algebraic topology, representation theory, and quantum physics. In this paper, we present analogous definitions for Lie algebras within the framework of whiskered structures, bimorphisms, crossed complexes, crossed differential graded algebras, and tensor products. These definitions, given for groupoids in existing literature, have been adapted to establish a direct correspondence between these algebraic structures and Lie algebras. We show that a 2-truncation of the crossed differential graded Lie algebra, obtained from our adapted definitions, gives rise to a braided crossed module of Lie algebras. We also construct a functor to simplicial Lie algebras, enabling a systematic mapping between different Lie algebraic categories, which supports the validity of our adapted definitions and establishes their compatibility with established categories.

APA, Harvard, Vancouver, ISO, and other styles

8

Fernández-Fariña, A., and M. Ladra. "Braiding for categorical algebras and crossed modules of algebras I: Associative and Lie algebras." Journal of Algebra and Its Applications 19, no. 09 (2019): 2050176. http://dx.doi.org/10.1142/s0219498820501765.

Full text

Abstract:

In this paper, the categories of braided categorical associative algebras and braided crossed modules of associative algebras are studied. These structures are also correlated with the categories of braided categorical Lie algebras and braided crossed modules of Lie algebras.

APA, Harvard, Vancouver, ISO, and other styles

9

Fernández-Fariña, Alejandro, and Manuel Ladra. "Braiding for categorical algebras and crossed modules of algebras II: Leibniz algebras." Filomat 34, no. 5 (2020): 1443–69. http://dx.doi.org/10.2298/fil2005443f.

Full text

Abstract:

In this paper, we study the category of braided categorical Leibniz algebras and braided crossed modules of Leibniz algebras, and we relate these structures with the categories of braided categorical Lie algebras and braided crossed modules of Lie algebras using the Loday-Pirashvili category.

APA, Harvard, Vancouver, ISO, and other styles

10

Arvasi, Z., M. Koçak, and E. Ulualan. "BRAIDED CROSSED MODULES AND REDUCED SIMPLICIAL GROUPS." Taiwanese Journal of Mathematics 9, no. 3 (2005): 477–88. http://dx.doi.org/10.11650/twjm/1500407855.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Quang, N. T., C. T. K. Phung та P. T. Cuc. "Braided equivariant crossed modules and cohomology of Γ-modules". Indian Journal of Pure and Applied Mathematics 45, № 6 (2014): 953–75. http://dx.doi.org/10.1007/s13226-014-0098-z.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Liu, Huili, Tao Yang, and Lingli Zhu. "Yetter–Drinfeld Modules for Group-Cograded Hopf Quasigroups." Mathematics 10, no. 9 (2022): 1388. http://dx.doi.org/10.3390/math10091388.

Full text

Abstract:

Let H be a crossed group-cograded Hopf quasigroup. We first introduce the notion of p-Yetter–Drinfeld quasimodule over H. If the antipode of H is bijective, we show that the category YDQ(H) of Yetter–Drinfeld quasimodules over H is a crossed category, and the subcategory YD(H) of Yetter–Drinfeld modules is a braided crossed category.

APA, Harvard, Vancouver, ISO, and other styles

13

Zhou, Xuan, and Tao Yang. "New BraidedT-Categories over Weak Crossed Hopf Group Coalgebras." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/626394.

Full text

Abstract:

LetHbe a weak crossed Hopf group coalgebra over groupπ; we first introduce a kind of newα-Yetter-Drinfel’d module categories𝒲𝒴𝒟α(H)forα∈πand use it to construct a braidedT-category𝒲𝒴𝒟(H). As an application, we give the concept of a Long dimodule categoryH𝒲ℒHfor a weak crossed Hopf group coalgebraHwith quasitriangular and coquasitriangular structures and obtain thatH𝒲ℒHis a braidedT-category by translating it into a weak Yetter-Drinfel'd module subcategory𝒲𝒴𝒟(H⊗H).

APA, Harvard, Vancouver, ISO, and other styles

14

Bespalov, Yuri, and Bernhard Drabant. "Hopf (bi-)modules and crossed modules in braided monoidal categories." Journal of Pure and Applied Algebra 123, no. 1-3 (1998): 105–29. http://dx.doi.org/10.1016/s0022-4049(96)00105-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

ODABAŞ, Alper, and Erdal ULUALAN. "Braided regular crossed modules bifibered over regular groupoids." TURKISH JOURNAL OF MATHEMATICS 41 (2017): 1385–403. http://dx.doi.org/10.3906/mat-1604-63.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Bespalov, Yu N. "Crossed modules, quantum braided groups, and ribbon structures." Theoretical and Mathematical Physics 103, no. 3 (1995): 621–37. http://dx.doi.org/10.1007/bf02065863.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

FUKUSHI, Takeo. "Perfect braided crossed modules and their mod-q analogues." Hokkaido Mathematical Journal 27, no. 1 (1998): 135–46. http://dx.doi.org/10.14492/hokmj/1351001255.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Arvasi, Z., and E. Ulualan. "3-types of simplicial groups and braided regular crossed modules." Homology, Homotopy and Applications 9, no. 1 (2007): 139–61. http://dx.doi.org/10.4310/hha.2007.v9.n1.a5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Zhu, Haixing. "The crossed structure of Hopf bimodules." Journal of Algebra and Its Applications 17, no. 09 (2018): 1850172. http://dx.doi.org/10.1142/s0219498818501724.

Full text

Abstract:

Let [Formula: see text] be a Hopf algebra with bijective antipode. We first define some generalized Hopf bimodules. Next, we show that these Hopf bimodules form a new tensor category with a crossed structure, which is equivalent to the category of some generalized Yetter–Drinfeld modules introduced by Panaite and Staic. Finally, based on this equivalence, we verify that the category of Hopf bimodules admits the structure of a braided [Formula: see text]-category in the sense of Turaev.

APA, Harvard, Vancouver, ISO, and other styles

20

Laugwitz, Robert. "Comodule algebras and 2-cocycles over the (Braided) Drinfeld double." Communications in Contemporary Mathematics 21, no. 04 (2019): 1850045. http://dx.doi.org/10.1142/s0219199718500451.

Full text

Abstract:

We show that for dually paired bialgebras, every comodule algebra over one of the paired bialgebras gives a comodule algebra over their Drinfeld double via a crossed product construction. These constructions generalize to working with bialgebra objects in a braided monoidal category of modules over a quasitriangular Hopf algebra. Hence two ways to provide comodule algebras over the braided Drinfeld double (the double bosonization) are provided. Furthermore, a map of second Hopf algebra cohomology spaces is constructed. It takes a pair of 2-cocycles over dually paired Hopf algebras and produces a 2-cocycle over their Drinfeld double. This construction also has an analogue for braided Drinfeld doubles.

APA, Harvard, Vancouver, ISO, and other styles

21

HASEGAWA, MASAHITO. "A quantum double construction in Rel." Mathematical Structures in Computer Science 22, no. 4 (2012): 618–50. http://dx.doi.org/10.1017/s0960129511000703.

Full text

Abstract:

We study bialgebras and Hopf algebras in the compact closed categoryRelof sets and binary relations. Various monoidal categories with extra structure arise as the categories of (co)modules of bialgebras and Hopf algebras inRel. In particular, for any groupG, we derive a ribbon category of crossedG-sets as the category of modules of a Hopf algebra inRelthat is obtained by the quantum double construction. This category of crossedG-sets serves as a model of the braided variant of propositional linear logic.

APA, Harvard, Vancouver, ISO, and other styles

22

Chen, Quanguo, and Dingguo Wang. "Constructing New Crossed Group Categories Over Weak Hopf Group Algebras." Mathematica Slovaca 65, no. 3 (2015). http://dx.doi.org/10.1515/ms-2015-0035.

Full text

Abstract:

AbstractLet π be a group. The main purpose of this paper is to provide further examples of crossed π-categories in the sense of Turaev. For this, we first introduce the notion of weak Hopf π-algebra as the dual notion of weak Hopf π-coalgebra and investigate the properties of weak Hopf π-algebra keeping close to weak Hopf algebra in sense of Böhm et al. It is shown that the category of the copresentations of weak Hopf π-algebra is braided crossed π-category. Finally, we shall consider the notion of weak Doi-Hopf group module in the weak Hopf π-algebra setting, and discuss the separability of a class of functors for the category of weak Doi-Hopf π-modules to the category of comodule over a suitable coalgebras. Also, the applications of our theories are presented.

APA, Harvard, Vancouver, ISO, and other styles

23

Gui, Bin. "Genus-zero permutation-twisted conformal blocks for tensor product vertex operator algebras: The tensor-factorizable case." Communications in Contemporary Mathematics, March 13, 2025. https://doi.org/10.1142/s0219199725500348.

Full text

Abstract:

Let [Formula: see text] be a vertex operator algebra (VOA), let [Formula: see text] be a finite set, and let [Formula: see text] be a subgroup of the permutation group [Formula: see text] which acts on [Formula: see text] in a natural way. For each [Formula: see text], the [Formula: see text]-twisted [Formula: see text]-modules were first constructed and characterized in [K. Barron, C. Dong and G. Mason, Twisted sectors for tensor product vertex operator algebras associated to permutation groups, Comm. Math. Phys. 227(2) (2002) 349–384] when [Formula: see text] has only one orbit, i.e. [Formula: see text] for some [Formula: see text]. In general, if [Formula: see text] is a disjoint union of several [Formula: see text]-orbits [Formula: see text], and if for each orbit [Formula: see text] one chooses a [Formula: see text]-twisted [Formula: see text]-module [Formula: see text], then [Formula: see text] is a [Formula: see text]-twisted [Formula: see text]-module. A direct sum of such [Formula: see text] is called a ⊗-factorizable [Formula: see text]-twisted [Formula: see text]-module. It is known that all [Formula: see text]-twisted modules are ⊗-factorizable if [Formula: see text] is rational [K. Barron, C. Dong and G. Mason, Twisted sectors for tensor product vertex operator algebras associated to permutation groups, Comm. Math. Phys. 227(2) (2002) 349–384]. In this paper, we use the main result of [B. Gui, Sewing and propagation of conformal blocks, New York J. Math. 30 (2024) 187–230] to construct an explicit isomorphism from the space of genus-[Formula: see text] conformal blocks associated to the [Formula: see text]-twisted [Formula: see text]-modules (i.e. [Formula: see text]-twisted [Formula: see text]-modules for some [Formula: see text]) that are ⊗-factorizable to the space of conformal blocks associated to the untwisted [Formula: see text]-modules and a branched covering [Formula: see text] of the Riemann sphere [Formula: see text]. When [Formula: see text] is CFT-type, [Formula: see text]-cofinite, and rational, we use the above result, the (untwisted) factorization property [C. Damiolini, A. Gibney and N. Tarasca, On factorization and vector bundles of conformal blocks from vertex algebras, Ann. Sci. École Norm. Sup. (2022)], and the Riemann–Hurwitz formula to completely determine the fusion rules among [Formula: see text]-twisted [Formula: see text]-modules. Furthermore, assuming [Formula: see text] is as above, we prove that the sewing/factorization of genus-[Formula: see text] [Formula: see text]-twisted [Formula: see text]-conformal blocks holds, and corresponds to the sewing/factorization of untwisted [Formula: see text]-conformal blocks associated to the branched coverings of [Formula: see text]. This proves, in particular, the operator product expansion (i.e. associativity) of [Formula: see text]-twisted [Formula: see text]-intertwining operators (a key ingredient of the [Formula: see text]-crossed braided tensor category [Formula: see text] of the [Formula: see text]-twisted [Formula: see text]-modules) without assuming that the fixed point subalgebra [Formula: see text] is [Formula: see text]-cofinite (and rational), a condition known so far only when [Formula: see text] is solvable and remains a conjecture in the general case. More importantly, this result implies that besides the fusion rules, the associativity isomorphism of [Formula: see text] is also characterized by the higher genus data of untwisted [Formula: see text]-conformal blocks, which gives a new insight into the category [Formula: see text]. We also discuss the applications to conformal nets, which are indeed the original motivations for the author to study the subject of this paper.

APA, Harvard, Vancouver, ISO, and other styles

24

Huebschmann, J. "Braids and crossed modules." Journal of Group Theory 15, no. 1 (2012). http://dx.doi.org/10.1515/jgt.2011.095.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

LADRA, Manuel, and Alejandro FERNÁNDEZ-FARİÑA. "UNIVERSAL CENTRAL EXTENSIONS OF BRAIDED LIE CROSSED MODULES." Hacettepe Journal of Mathematics and Statistics, December 31, 2022, 1–16. http://dx.doi.org/10.15672/hujms.901199.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Casas, José Manuel, Alejandro Fernández-Fariña, and Manuel Ladra. "Universal central extensions of braided crossed modules of groups." Journal of Pure and Applied Algebra, May 2024, 107715. http://dx.doi.org/10.1016/j.jpaa.2024.107715.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Majid, Shahn, and Leo Sean McCormack. "Quantum geometric Wigner construction for D(G) and braided racks." Journal of Mathematical Physics 66, no. 6 (2025). https://doi.org/10.1063/5.0248703.

Full text

Abstract:

The quantum double of a finite group plays an important role in the Kitaev model for quantum computing, as well as in associated topological quantum field theories, as a kind of Poincaré group. We interpret the known construction of its irreps, which are quasiparticles for the model, in a geometric manner strictly analogous to the Wigner construction for the usual Poincaré group of R1,3. Irreps are labeled by pairs (C,π), where C is a conjugacy class in the role of a mass-shell, and π is a representation of the isotropy group CG in the role of spin. The geometric picture entails as a quantum homogeneous bundle where the base is G/CG, and D∨(G)→C(G) as another homogeneous bundle with base the group algebra CG as noncommutative spacetime. Analysis of the latter leads to a duality whereby the differential calculus and solutions of the wave equation on CG are governed by irreps and conjugacy classes of G respectively, while the same picture on C(G) is governed by the reversed data. Quasiparticles as irreps of D(G) also turn out to classify irreducible bicovariant differential structures ΩC,π1 on D∨(G) and these in turn correspond to braided-Lie algebras LC,π in the braided category of G-crossed modules, which we call “braided racks” and study. We show under mild assumptions that U(LC,π) quotients to a braided Hopf algebra BC,π related by transmutation to a coquasitriangular Hopf algebra HC,π.

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!