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Journal articles on the topic 'Non-commutative topology'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

Solovyov, Sergey A. "Generalized fuzzy topology versus non-commutative topology." Fuzzy Sets and Systems 173, no. 1 (2011): 100–115. http://dx.doi.org/10.1016/j.fss.2011.03.005.

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2

Bauer, Andrej, Karin Cvetko-Vah, Mai Gehrke, Samuel J. van Gool, and Ganna Kudryavtseva. "A non-commutative Priestley duality." Topology and its Applications 160, no. 12 (2013): 1423–38. http://dx.doi.org/10.1016/j.topol.2013.05.012.

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3

Wu, Wei. "Non-commutative metric topology on matrix state space." Proceedings of the American Mathematical Society 134, no. 02 (2005): 443–53. http://dx.doi.org/10.1090/s0002-9939-05-08036-6.

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4

Goldstein, Stanisław. "Conditional expectation and stochastic integrals in non-commutative Lp spaces." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 2 (1991): 365–83. http://dx.doi.org/10.1017/s0305004100070432.

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The aim of the paper is to propose a general scheme for the consideration of non-commutative stochastic integrals. The role of a probability space is played by a couple (, φ0), where is a von Neumann algebra and φ0 is a faithful normal state on . Our processes live in the algebra of all measurable operators associated with the crossed product of by the modular automorphism group The algebra contains all the (Haagerup's) Lp spaces over . The measure topology of the algebra has the nice feature of inducing the Lp norm topology on the Lp spaces, which makes it particularly suitable for defining s

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5

Schweizer, J. "An Analogue of Peetre's Theorem in Non-Commutative Topology." Quarterly Journal of Mathematics 52, no. 4 (2001): 499–506. http://dx.doi.org/10.1093/qjmath/52.4.499.

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6

De Nittis, Giuseppe, and Hermann Schulz-Baldes. "The non-commutative topology of two-dimensional dirty superconductors." Journal of Geometry and Physics 124 (January 2018): 100–123. http://dx.doi.org/10.1016/j.geomphys.2017.10.016.

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7

Georgescu, G., and A. Popescu. "Non-commutative fuzzy Galois connections." Soft Computing 7, no. 7 (2003): 458–67. http://dx.doi.org/10.1007/s00500-003-0280-4.

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8

GAROUFALIDIS, STAVROS, and XINYU SUN. "THE NON-COMMUTATIVE A-POLYNOMIAL OF TWIST KNOTS." Journal of Knot Theory and Its Ramifications 19, no. 12 (2010): 1571–95. http://dx.doi.org/10.1142/s021821651000856x.

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The purpose of the paper is two-fold: to introduce a multivariable creative telescoping method, and to apply it in a problem of Quantum Topology: namely the computation of the non-commutative A-polynomial of twist knots. Our multivariable creative telescoping method allows us to compute linear recursions for sums of the form [Formula: see text] given a recursion relation for [Formula: see text] and the hypergeometric kernel c(n, k). As an application of our method, we explicitly compute the non-commutative A-polynomial for twist knots with -15 and 15 crossings. The non-commutative A-polynomial

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9

Junge, M. "Embeddings of non-commutative L p -spaces into non-commutative L 1 -spaces, 1 < p < 2." Geometric And Functional Analysis 10, no. 2 (2000): 389–406. http://dx.doi.org/10.1007/s000390050012.

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10

Szendrői, Balázs. "Non-commutative Donaldson–Thomas invariants and the conifold." Geometry & Topology 12, no. 2 (2008): 1171–202. http://dx.doi.org/10.2140/gt.2008.12.1171.

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11

Nagao, Kentaro. "Non-commutative Donaldson–Thomas theory and vertex operators." Geometry & Topology 15, no. 3 (2011): 1509–43. http://dx.doi.org/10.2140/gt.2011.15.1509.

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12

Andr�, Johannes. "Non-commutative spaces with transitive translation groups. II." Geometriae Dedicata 58, no. 1 (1995): 63–73. http://dx.doi.org/10.1007/bf01263476.

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13

Sukochev, F., K. Tulenov, and D. Zanin. "Nehari-Type Theorem for Non-commutative Hardy Spaces." Journal of Geometric Analysis 27, no. 3 (2016): 1789–802. http://dx.doi.org/10.1007/s12220-016-9740-9.

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14

Francot, Eliana. "Unitary polarities in non commutative twisted field planes." Journal of Geometry 70, no. 1 (2001): 59–65. http://dx.doi.org/10.1007/pl00000993.

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15

Pfalzgraf, Jochen. "On a model for non commutative geometric spaces." Journal of Geometry 25, no. 2 (1985): 147–63. http://dx.doi.org/10.1007/bf01220477.

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16

Huber, Beatrix, and Tim Netzer. "A note on non-commutative polytopes and polyhedra." Advances in Geometry 21, no. 1 (2021): 119–24. http://dx.doi.org/10.1515/advgeom-2020-0029.

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Abstract It is well-known that every polyhedral cone is finitely generated (i.e. polytopal), and vice versa. Surprisingly, the two notions differ almost always for non-commutative versions of such cones, as was recently proved by different authors. In this note we give a direct and constructive proof of the statement. Our proof yields a new and surprising quantitative result: the difference of the two notions can always be seen at the first level of non-commutativity, i.e. for matrices of size 2, independent of dimension and complexity of the initial convex cone.

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17

Rennemo, Jørgen Vold, Ed Segal, and Michel Van den Bergh. "A non-commutative Bertini theorem." Journal of Noncommutative Geometry 13, no. 2 (2019): 609–16. http://dx.doi.org/10.4171/jncg/334.

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18

Beggs, Edwin, and S. Paul Smith. "Non-commutative complex differential geometry." Journal of Geometry and Physics 72 (October 2013): 7–33. http://dx.doi.org/10.1016/j.geomphys.2013.03.018.

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19

H�jek, P. "Observations on non-commutative fuzzy logic." Soft Computing - A Fusion of Foundations, Methodologies and Applications 8, no. 1 (2003): 38–43. http://dx.doi.org/10.1007/s00500-002-0246-y.

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20

Harvey, Shelly L., and Stefan Friedl. "Non-commutative multivariable Reidemester torsion and the Thurston norm." Algebraic & Geometric Topology 7, no. 2 (2007): 755–77. http://dx.doi.org/10.2140/agt.2007.7.755.

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21

Fernandes, Rui Loja, Camille Laurent-Gengoux, and Pol Vanhaecke. "Global action-angle variables for non-commutative integrable systems." Journal of Symplectic Geometry 16, no. 3 (2018): 645–99. http://dx.doi.org/10.4310/jsg.2018.v16.n3.a3.

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22

Rump, Wolfgang. "Multi-posets in algebraic logic, group theory, and non-commutative topology." Annals of Pure and Applied Logic 167, no. 11 (2016): 1139–60. http://dx.doi.org/10.1016/j.apal.2016.05.001.

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23

Colombo, Fabrizio, Graziano Gentili, Irene Sabadini, and Daniele C. Struppa. "Non-commutative functional calculus: Unbounded operators." Journal of Geometry and Physics 60, no. 2 (2010): 251–59. http://dx.doi.org/10.1016/j.geomphys.2009.09.011.

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24

Sukochev, Fedor, and Alexandr Usachev. "Dixmier traces and non-commutative analysis." Journal of Geometry and Physics 105 (July 2016): 102–22. http://dx.doi.org/10.1016/j.geomphys.2016.03.010.

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25

Ciungu, Lavinia Corina. "Relative negations in non-commutative fuzzy structures." Soft Computing 18, no. 1 (2013): 15–33. http://dx.doi.org/10.1007/s00500-013-1054-2.

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26

Ansari-Toroghy, Habibollah, Shokoufeh Habibi, and Masoomeh Hezarjaribi. "On the graph of modules over commutative rings II." Filomat 32, no. 10 (2018): 3657–65. http://dx.doi.org/10.2298/fil1810657a.

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Let M be a module over a commutative ring R. In this paper, we continue our study about the quasi-Zariski topology-graph G(?*T) which was introduced in (On the graph of modules over commutative rings, Rocky Mountain J. Math. 46(3) (2016), 1-19). For a non-empty subset T of Spec(M), we obtain useful characterizations for those modules M for which G(?*T) is a bipartite graph. Also, we prove that if G(?*T) is a tree, then G(?*T) is a star graph. Moreover, we study coloring of quasi-Zariski topology-graphs and investigate the interplay between ?(G(?+T)) and ?(G(?+T)).

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27

Popescu, Gelu. "Andô dilations and inequalities on non-commutative domains." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, no. 6 (2018): 1239–67. http://dx.doi.org/10.1017/s030821051800015x.

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We obtain intertwining dilation theorems for non-commutative regular domains 𝒟f and non-commutative varieties 𝒱J in B(𝓗)n, which generalize Sarason and Szőkefalvi-Nagy and Foiaş's commutant lifting theorem for commuting contractions. We present several applications including a new proof for the commutant lifting theorem for pure elements in the domain 𝒟f (respectively, variety 𝒱J ) as well as a Schur-type representation for the unit ball of the Hardy algebra associated with the variety 𝒱J. We provide Andô-type dilations and inequalities for bi-domains 𝒟f ×c 𝒟g consisting of all pairs (X,Y ) of

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28

Kawamura, Katsunori. "Serre–Swan theorem for non-commutative -algebras." Journal of Geometry and Physics 48, no. 2-3 (2003): 275–96. http://dx.doi.org/10.1016/s0393-0440(03)00044-5.

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29

Gurevich, D., R. Leclercq, and P. Saponov. "q-Index on braided non-commutative spheres." Journal of Geometry and Physics 53, no. 4 (2005): 392–420. http://dx.doi.org/10.1016/j.geomphys.2004.07.007.

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30

Somaglia, Jacopo. "On the class of continuous images of non-commutative Valdivia compacta." Topology and its Applications 210 (September 2016): 147–67. http://dx.doi.org/10.1016/j.topol.2016.07.012.

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31

Benameur, Moulay-Tahar, and James L. Heitsch. "Index Theory and Non-Commutative Geometry II. Dirac Operators and Index Bundles." Journal of K-Theory 1, no. 2 (2007): 305–56. http://dx.doi.org/10.1017/is007011012jkt007.

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AbstractWhen the index bundle of a longitudinal Dirac type operator is transversely smooth, we define its Chern character in Haefliger cohomology and relate it to the Chern character of the K—theory index. This result gives a concrete connection between the topology of the foliation and the longitudinal index formula. Moreover, the usual spectral assumption on the Novikov-Shubin invariants of the operator is improved.

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32

Nechaev, S. K. "Problems of probabilistic topology: the statistics of knots and non-commutative random walks." Physics-Uspekhi 41, no. 4 (1998): 313–47. http://dx.doi.org/10.1070/pu1998v041n04abeh000382.

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33

Nechaev, S. K. "Problems of probabilistic topology: the statistics of knots and non-commutative random walks." Uspekhi Fizicheskih Nauk 168, no. 4 (1998): 369. http://dx.doi.org/10.3367/ufnr.0168.199804a.0369.

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34

Coates, John, Takako Fukaya, Kazuya Kato, and Ramdorai Sujatha. "Root numbers, Selmer groups, and non-commutative Iwasawa theory." Journal of Algebraic Geometry 19, no. 1 (2010): 19–97. http://dx.doi.org/10.1090/s1056-3911-09-00504-9.

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35

Aschenbrenner, Matthias, Anatole Khélif, Eudes Naziazeno, and Thomas Scanlon. "The Logical Complexity of Finitely Generated Commutative Rings." International Mathematics Research Notices 2020, no. 1 (2018): 112–66. http://dx.doi.org/10.1093/imrn/rny023.

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AbstractWe characterize those finitely generated commutative rings which are (parametrically) bi-interpretable with arithmetic: a finitely generated commutative ring A is bi-interpretable with $(\mathbb{N},{+},{\times })$ if and only if the space of non-maximal prime ideals of A is nonempty and connected in the Zariski topology and the nilradical of A has a nontrivial annihilator in $\mathbb{Z}$. Notably, by constructing a nontrivial derivation on a nonstandard model of arithmetic we show that the ring of dual numbers over $\mathbb{Z}$ is not bi-interpretable with $\mathbb{N}$.

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36

Serre, Denis. "Non-commutative standard polynomials applied to matrices." Linear Algebra and its Applications 490 (February 2016): 202–23. http://dx.doi.org/10.1016/j.laa.2015.11.003.

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37

Wang, Hsin-Ju. "Co-maximal graph of non-commutative rings." Linear Algebra and its Applications 430, no. 2-3 (2009): 633–41. http://dx.doi.org/10.1016/j.laa.2008.08.026.

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38

LEIGH, ROBERT G. "MARGINAL DEFORMATIONS OF N=4 SYM AND NON-COMMUTATIVE MODULI SPACES OF VACUA." International Journal of Modern Physics A 16, supp01c (2001): 955–57. http://dx.doi.org/10.1142/s0217751x0100859x.

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We review recent work on the application of the non-commutative geometric framework to an interpretation of the moduli space of vacua of marginal deformations of N = 4 super Yang-Mills theories. At rational values of couplings, different regions of moduli space may be associated with D5-branes of various topologies, and orbifold dual descriptions exist which may be accessed by T-duality. Singularities in the moduli space are associated with topology change.

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39

Špenko, Špela, and Michel Van den Bergh. "Non-commutative crepant resolutions for some toric singularities. II." Journal of Noncommutative Geometry 14, no. 1 (2020): 73–103. http://dx.doi.org/10.4171/jncg/359.

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40

Rachůnek, J. "Compactness in MV-algebras and in their non-commutative generalizations." Soft Computing 7, no. 7 (2003): 482–85. http://dx.doi.org/10.1007/s00500-003-0284-0.

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41

Eslami, Esfandiar, Hamid Khosravi, and Faramarz Sadeghi. "Very and more or less in non-commutative fuzzy logic." Soft Computing 12, no. 3 (2007): 275–79. http://dx.doi.org/10.1007/s00500-007-0199-2.

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42

Ghasemi, Mehdi, Murray Marshall та Sven Wagner. "Closure of the Cone of Sums of 2d-powers in Certain Weighted ℓ1-seminorm Topologies". Canadian Mathematical Bulletin 57, № 2 (2014): 289–302. http://dx.doi.org/10.4153/cmb-2012-043-9.

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AbstractIn a paper from 1976, Berg, Christensen, and Ressel prove that the closure of the cone of sums of squares in the polynomial ring in the topology induced by the ℓ1-norm is equal to Pos([–1; 1]n), the cone consisting of all polynomials that are non-negative on the hypercube [–1,1]n. The result is deduced as a corollary of a general result, established in the same paper, which is valid for any commutative semigroup. In later work, Berg and Maserick and Berg, Christensen, and Ressel establish an even more general result, for a commutative semigroup with involution, for the closure of the c

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43

Ferleger, Sergei V., and Fyodor A. Sukochev. "On the contractibility to a point of the linear groups of reflexive non-commutative Lp-spaces." Mathematical Proceedings of the Cambridge Philosophical Society 119, no. 3 (1996): 545–60. http://dx.doi.org/10.1017/s0305004100074405.

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For every Banach space X, denote by GL(X) the linear group of X, i.e. the group of all linear continuous invertible operators on X with the topology induced by the operator norm. One says that GL(X) is contractible to a point if there exists a continuous map F: GL(X) × [0, 1] → GL(X) such that F(A,0) = A and F(A, 1) = Id, for every A ∈ GL(X).

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44

Bonechi, F., N. Ciccoli, L. Dąbrowski, and M. Tarlini. "Bijectivity of the canonical map for the non-commutative instanton bundle." Journal of Geometry and Physics 51, no. 1 (2004): 71–81. http://dx.doi.org/10.1016/j.geomphys.2003.09.007.

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45

Kim, Se-Jin, and Arthur Mehta. "Chromatic numbers, Sabidussi's Theorem and Hedetniemi's conjecture for non-commutative graphs." Linear Algebra and its Applications 582 (December 2019): 291–309. http://dx.doi.org/10.1016/j.laa.2019.08.002.

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46

Miller, John Boris. "The natural ordering on a strictly real Banach algebra." Mathematical Proceedings of the Cambridge Philosophical Society 107, no. 3 (1990): 539–56. http://dx.doi.org/10.1017/s0305004100068808.

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AbstractA strictly real unital Banach algebra is one in which every element has real spectrum. An antilattice partial order and its associated open-interval topology are defined on by taking as positive cone the principal component of the maximal group of the algebra, and their properties are studied. The topology coincides with the semimetric topology of the spectral radius, which is a seminorm, making into a locally convex partially ordered topological algebra with continuous inversion and normal cone. Every positive element has a unique positive square root, and logarithm, and these functio

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47

Zuo, Weibing. "On the relationships between hybrid generalized Bosbach states and L-filters in non-commutative residuated lattices." Soft Computing 23, no. 17 (2019): 7537–55. http://dx.doi.org/10.1007/s00500-018-03747-w.

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48

Iorgulescu, Afrodita. "Classes of examples of pseudo-MV algebras, pseudo-BL algebras and divisible bounded non-commutative residuated lattices." Soft Computing 14, no. 4 (2009): 313–27. http://dx.doi.org/10.1007/s00500-009-0405-5.

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49

Kassem, M. S., and K. Rowlands. "The quasi-strict topology on the space of quasi-multipliers of a B*-algebra." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 3 (1987): 555–66. http://dx.doi.org/10.1017/s0305004100066913.

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The notion of a left (right, double) multiplier may be regarded as a generalization of the concept of a multiplier to a non-commutative Banach algebra. Each of these is a special case of a more general object, namely that of a quasi-multiplier. The idea of a quasi-multiplier was first introduced by Akemann and Pedersen in ([1], §4), where they consider the quasi-multipliers of a C*-algebra. One of the defects of quasi-multipliers is that, at least a priori, there does not appear to be a way of multiplying them together. The general theory of quasi-multipliers of a Banach algebra A with an appr

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50

Durand, Philippe. "Mathematical Tools to Understand the Field Theories of the Standard Model and Beyond." International Journal of Mathematics and Computers in Simulation 15 (July 28, 2021): 54–61. http://dx.doi.org/10.46300/9102.2021.15.10.

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Since Isaac Newton the understanding of the physical world is more and more complex. The Euclidean space of three dimensions , independent of time is replaced in Enstein’s vision by the Lorentzian space-time at first, then by four dimensions manifold to unify space and matter. String theorists add to space more dimensions to make their theory consistent. Complex topological invariants which characterize different kind of spaces are developed. Space is discretized at the quantum scale in the loop quantum gravity theory. A non-commutative and spectral geometry is defined from the theory of opera

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