2015, Mathematical surveys and monographs, ISBN 1470420244, Volume no. 205., xvi, 343

Book

Applied Categorical Structures, ISSN 0927-2852, 12/2017, Volume 25, Issue 6, pp. 1199 - 1228

We prove that if a finite tensor category $${\mathcal C}$$ C is symmetric, then the monoidal category of one-sided $${\mathcal C...

Braided monoidal category | Mathematics | Theory of Computation | Brauer–Picard group | Cohomology | 18D05 | Geometry | 19D23 | 18D10 | 18D35 | 19A99 | Convex and Discrete Geometry | Finite tensor category | Mathematical Logic and Foundations | Picard group | MATHEMATICS | FUSION CATEGORIES | TRIANGULAR HOPF-ALGEBRAS | BIMODULE CATEGORIES | BRAUER GROUP | Brauer-Picard group

Braided monoidal category | Mathematics | Theory of Computation | Brauer–Picard group | Cohomology | 18D05 | Geometry | 19D23 | 18D10 | 18D35 | 19A99 | Convex and Discrete Geometry | Finite tensor category | Mathematical Logic and Foundations | Picard group | MATHEMATICS | FUSION CATEGORIES | TRIANGULAR HOPF-ALGEBRAS | BIMODULE CATEGORIES | BRAUER GROUP | Brauer-Picard group

Journal Article

Selecta mathematica (Basel, Switzerland), ISSN 1420-9020, 2010, Volume 16, Issue 1, pp. 1 - 119

We introduce a new notion of the core of a braided fusion category. It allows to separate the part of a braided fusion category that does not come from finite groups...

18D10 | Tensor category | Equivariantization | 16W30 | Braided tensor category | Mathematics, general | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | EXTENSIONS | SUBFACTORS | TENSOR CATEGORIES

18D10 | Tensor category | Equivariantization | 16W30 | Braided tensor category | Mathematics, general | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | EXTENSIONS | SUBFACTORS | TENSOR CATEGORIES

Journal Article

Algebra and Number Theory, ISSN 1937-0652, 2013, Volume 7, Issue 6, pp. 1365 - 1403

For a finite braided tensor category C we introduce its Picard crossed module P(C) consisting of the group of invertible C-module categories and the group of braided tensor autoequivalences of C...

Invertible module category | Braided autoequivalence | Braided tensor category | Drinfeld center | MATHEMATICS | invertible module category | ALGEBRAS | BRAUER GROUP | braided tensor category | EQUIVALENCE | braided autoequivalence

Invertible module category | Braided autoequivalence | Braided tensor category | Drinfeld center | MATHEMATICS | invertible module category | ALGEBRAS | BRAUER GROUP | braided tensor category | EQUIVALENCE | braided autoequivalence

Journal Article

Journal of Algebra, ISSN 0021-8693, 08/2013, Volume 388, pp. 374 - 396

In this paper we study the relative tensor product of module categories over braided fusion categories using, in part, the notion of the relative center of a bimodule category...

Tensor categories | Representation theory | Braided fusion categories | MATHEMATICS

Tensor categories | Representation theory | Braided fusion categories | MATHEMATICS

Journal Article

Tohoku Mathematical Journal, ISSN 0040-8735, 09/2016, Volume 68, Issue 3, pp. 377 - 405

We introduce the notion of (G, Gamma)-crossed action on a tensor category, where (G, Gamma) is a matched pair of finite groups...

Tensor category | Exact sequence | Crossed braiding | Braided tensor category | Crossed action | Matched pair | SET-THEORETICAL SOLUTIONS | MATHEMATICS | YANG-BAXTER EQUATION | matched pair | HOPF-ALGEBRAS | exact sequence | EXTENSIONS | braided tensor category | crossed braiding | crossed action

Tensor category | Exact sequence | Crossed braiding | Braided tensor category | Crossed action | Matched pair | SET-THEORETICAL SOLUTIONS | MATHEMATICS | YANG-BAXTER EQUATION | matched pair | HOPF-ALGEBRAS | exact sequence | EXTENSIONS | braided tensor category | crossed braiding | crossed action

Journal Article

Journal of Algebra, ISSN 0021-8693, 10/2017, Volume 487, pp. 118 - 137

We prove a coherence theorem for actions of groups on monoidal categories. As an application we prove coherence for arbitrary braided G-crossed categories.

Fusion categories | Braided G-crossed categories | Action of groups on categories | Tensor categories | MATHEMATICS | MODULES | Mathematics - Quantum Algebra

Fusion categories | Braided G-crossed categories | Action of groups on categories | Tensor categories | MATHEMATICS | MODULES | Mathematics - Quantum Algebra

Journal Article

2013, Volume 585

Conference Proceeding

Advances in mathematics (New York. 1965), ISSN 0001-8708, 2011, Volume 226, Issue 1, pp. 176 - 205

We introduce two new classes of fusion categories which are obtained by a certain procedure from finite groups...

Fusion categories | Braided fusion categories | Semisimple Hopf algebras | Solvable fusion categories | Group-theoretical fusion categories | Categorical Morita equivalence | MATHEMATICS | INVARIANTS | MODULE CATEGORIES | BRAIDED TENSOR CATEGORIES | CLASSIFICATION | SEMISIMPLE HOPF-ALGEBRAS

Fusion categories | Braided fusion categories | Semisimple Hopf algebras | Solvable fusion categories | Group-theoretical fusion categories | Categorical Morita equivalence | MATHEMATICS | INVARIANTS | MODULE CATEGORIES | BRAIDED TENSOR CATEGORIES | CLASSIFICATION | SEMISIMPLE HOPF-ALGEBRAS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 11/2013, Volume 247, pp. 192 - 265

Starting with a self-dual Hopf algebra H in a braided monoidal category S we construct a Z/2Z-graded monoidal category C=C0+C1...

Braided monoidal categories | Hopf algebras and their representations | MATHEMATICS | FINITE WATATANI INDEXES | WEYL GROUP | C-ASTERISK-ALGEBRAS | BRAIDED TENSOR CATEGORIES | MULTIPLICATIVE FORMULA | CLASSIFICATION | SUBALGEBRAS | SEMISIMPLE

Braided monoidal categories | Hopf algebras and their representations | MATHEMATICS | FINITE WATATANI INDEXES | WEYL GROUP | C-ASTERISK-ALGEBRAS | BRAIDED TENSOR CATEGORIES | MULTIPLICATIVE FORMULA | CLASSIFICATION | SUBALGEBRAS | SEMISIMPLE

Journal Article

International journal of mathematics, ISSN 1793-6519, 2018, Volume 29, Issue 2, p. 1850012

We show that the core of a weakly group-theoretical braided fusion category [Formula: see text] is equivalent as a braided fusion category to a tensor product...

weakly anisotropic braided fusion category | core of a fusion category | weakly group-Theoretical fusion category | braided G-crossed fusion category | Tannakian category | Braided fusion category | MATHEMATICS | weakly group-theoretical fusion category | TENSOR CATEGORIES

weakly anisotropic braided fusion category | core of a fusion category | weakly group-Theoretical fusion category | braided G-crossed fusion category | Tannakian category | Braided fusion category | MATHEMATICS | weakly group-theoretical fusion category | TENSOR CATEGORIES

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 04/2017, Volume 58, Issue 4, p. 41704

We study spin and super-modular categories systematically as inspired by fermionic topological phases of matter, which are always fermion parity enriched and modelled by spin topological quantum field...

FUSION CATEGORIES | HOPF-ALGEBRAS | INVARIANTS | SIMPLE CURRENTS | BRAIDED TENSOR CATEGORIES | ANYONS | PHYSICS, MATHEMATICAL | Fermions | Categories | Quotients | Gauging | Gaging | Parity | Quantum theory | Mathematics - Quantum Algebra

FUSION CATEGORIES | HOPF-ALGEBRAS | INVARIANTS | SIMPLE CURRENTS | BRAIDED TENSOR CATEGORIES | ANYONS | PHYSICS, MATHEMATICAL | Fermions | Categories | Quotients | Gauging | Gaging | Parity | Quantum theory | Mathematics - Quantum Algebra

Journal Article

Journal of Algebra, ISSN 0021-8693, 11/2017, Volume 489, pp. 264 - 309

We present an approach of calculating the group of braided autoequivalences of the category of representations of the Drinfeld double of a finite dimensional Hopf algebra H and thus the Brauer...

Fusion categories | Braided autoequivalences | Quantum algebra | Brauer–Picard group | Hopf–Galois extensions | Lazy cohomology | Brauer Picard group | HOPF-ALGEBRAS | MATHEMATICS | MODULE | COHOMOLOGY | Hopf-Galois extensions | FUNCTORS | SEQUENCE | TENSOR CATEGORY | Algebra

Fusion categories | Braided autoequivalences | Quantum algebra | Brauer–Picard group | Hopf–Galois extensions | Lazy cohomology | Brauer Picard group | HOPF-ALGEBRAS | MATHEMATICS | MODULE | COHOMOLOGY | Hopf-Galois extensions | FUNCTORS | SEQUENCE | TENSOR CATEGORY | Algebra

Journal Article

Selecta mathematica (Basel, Switzerland), ISSN 1420-9020, 2019, Volume 25, Issue 2, pp. 1 - 21

.... If the level satisfies a certain coprime property then it is even a modular tensor category. In all cases open Hopf links coincide with the corresponding normalized S-matrix entries of torus one-point functions...

17B67 | Mathematics, general | 18D19 | Mathematics | 17B69 | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATION-THEORY | VERLINDE FORMULAS | BRAIDED TENSOR CATEGORIES | COSETS | MODULAR DATA | RULES | CHARACTERS | Algebra

17B67 | Mathematics, general | 18D19 | Mathematics | 17B69 | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATION-THEORY | VERLINDE FORMULAS | BRAIDED TENSOR CATEGORIES | COSETS | MODULAR DATA | RULES | CHARACTERS | Algebra

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 06/2007, Volume 231, Issue 2, pp. 361 - 399

We extend subfactor constructions originally defined for unitary braid representations to the setting of braided C*-tensor categories...

Braided C tensor category | Subfactor | MATHEMATICS | subfactor | FUSION | GENERAL-THEORY | INVARIANTS | SECTORS | HECKE ALGEBRAS | 3-MANIFOLDS | braided C tensor category

Braided C tensor category | Subfactor | MATHEMATICS | subfactor | FUSION | GENERAL-THEORY | INVARIANTS | SECTORS | HECKE ALGEBRAS | 3-MANIFOLDS | braided C tensor category

Journal Article

New York Journal of Mathematics, 2008, Volume 14, pp. 261 - 284

Journal Article

Selecta Mathematica, ISSN 1022-1824, 3/2013, Volume 19, Issue 1, pp. 237 - 269

... to $${{\mathbb{Z}}/16\mathbb{Z}}$$ . Finally, we give a complete description of étale algebras in tensor products of braided fusion categories.

18D10 | 17B67 | Braided tensor category | Mathematics, general | Mathematics | Étale algebra | Witt group | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | Etale algebra | SUBFACTORS | MODULAR INVARIANTS | TENSOR CATEGORIES | Analysis | Algebra

18D10 | 17B67 | Braided tensor category | Mathematics, general | Mathematics | Étale algebra | Witt group | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | Etale algebra | SUBFACTORS | MODULAR INVARIANTS | TENSOR CATEGORIES | Analysis | Algebra

Journal Article

Algebra and Number Theory, ISSN 1937-0652, 2009, Volume 3, Issue 8, pp. 959 - 990

Let C be a fusion category faithfully graded by a finite group G and let D be the trivial component of this grading. The center L(C...

Fusion categories | Braided categories | Graded tensor categories | MATHEMATICS | SELF-DUALITY | HOPF-ALGEBRAS | INVARIANTS | braided categories | BRAIDED TENSOR CATEGORIES | fusion categories | RULES | graded tensor categories

Fusion categories | Braided categories | Graded tensor categories | MATHEMATICS | SELF-DUALITY | HOPF-ALGEBRAS | INVARIANTS | braided categories | BRAIDED TENSOR CATEGORIES | fusion categories | RULES | graded tensor categories

Journal Article

Journal of Algebra, ISSN 0021-8693, 03/2019, Volume 522, pp. 243 - 308

We study the universal Hopf algebra L of Majid and Lyubashenko in the case that the underlying ribbon category is the category of representations of a finite dimensional ribbon quasi-Hopf algebra A. We show that L...

Mapping class group representations | Quasi-Hopf algebras | Braided tensor categories | FUSION | REPRESENTATIONS | QUANTUM GROUPS | INVARIANTS | FORMULA | TENSOR CATEGORIES | INTEGRALS | MATHEMATICS | VERTEX OPERATOR-ALGEBRAS | 3-MANIFOLDS

Mapping class group representations | Quasi-Hopf algebras | Braided tensor categories | FUSION | REPRESENTATIONS | QUANTUM GROUPS | INVARIANTS | FORMULA | TENSOR CATEGORIES | INTEGRALS | MATHEMATICS | VERTEX OPERATOR-ALGEBRAS | 3-MANIFOLDS

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 12/2018, Volume 21, Issue 6, pp. 1353 - 1368

Let C $\mathcal {C}$ be a modular category of Frobenius-Perron dimension d q n , where q...

18D10 | Associative Rings and Algebras | Modular category | Group-theoretical fusion category | Non-associative Rings and Algebras | 16T05 | Commutative Rings and Algebras | Mathematics | Braided G -crossed fusion category | Tannakian category | Braided fusion category | Braided G-crossed fusion category | MATHEMATICS | FUSION CATEGORIES | HOPF-ALGEBRAS | DIMENSION PQ | BRAIDED TENSOR CATEGORIES

18D10 | Associative Rings and Algebras | Modular category | Group-theoretical fusion category | Non-associative Rings and Algebras | 16T05 | Commutative Rings and Algebras | Mathematics | Braided G -crossed fusion category | Tannakian category | Braided fusion category | Braided G-crossed fusion category | MATHEMATICS | FUSION CATEGORIES | HOPF-ALGEBRAS | DIMENSION PQ | BRAIDED TENSOR CATEGORIES

Journal Article

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