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On the equivalence of module categories over a group-theoretical fusion category
(Natl Acad Sci Ukraine, 2017-06)
We give a necessary and sufficient condition in terms of group cohomology for two indecomposable module categories over a group-theoretical fusion category C to be equivalent. This concludes the classification of such ...
On the Classification of Almost Square-Free Modular Categories
(Springer, 2017-11)
Let (Formula presented.) be a modular category of Frobenius-Perron dimension dqn, where q > 2 is a prime number and d is a square-free integer. We show that (Formula presented.) must be integral and nilpotent and therefore ...
Module categories over equivariantized tensor categories
(Independent Univ Moscow, 2017-03)
For a finite tensor category C and a Hopf monad T : C --> C satisfying certain conditions we describe exact indecomposable left C^T-module categories in terms of left C-module categories and some extra data. We also give ...
On weakly group-theoretical non-degenerate braided fusion categories
(European Mathematical Society, 2014-01)
We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. ...
COMMUTATIVE ALGEBRAS IN DRINFELD CATEGORIES OF ABELIAN LIE ALGEBRAS
(CAMBRIDGE UNIV PRESSNEW YORK, 2012)
We describe (braided-) commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe ...
Classification of Integral Modular Categories of Frobenius–Perron Dimension pq4 and p2q2
(Canadian Mathematical Soc, 2014-04)
We classify integral modular categories of dimension pq^4 and p^2q^2, where p and q are distinct primes. We show that such categories are always group-theoretical except for categories of dimension 4q^2. In these cases ...
Graphs attached to simple Frobenius-Perron dimensions of an integral fusion category
(Springer Wien, 2016-04)
Let (Formula presented.) be an integral fusion category. We study some graphs, called the prime graph and the common divisor graph, related to the Frobenius-Perron dimensions of simple objects in the category (Formula ...
Irreducible morphisms of categories of complexes
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2009)
We study irreducible morphisms of complexes. In particular, we show that the irreducible morphisms having one (finite) irreducible submorphism fall into three canonical forms and we give necessary and sufficient conditions ...
On fusion rules and solvability of a fusion category
(De Gruyter, 2017-01)
We address the question whether or not the condition on a fusion category being solvable is determined by its fusion rules. We prove that the answer is affirmative for some families of non-solvable examples arising from ...
Fundamental group of Schurian categories and the Hurewicz isomorphism
(Univ Bielefeld, 2011-06)
Let k be a field. We attach a CW-complex to any Schurian k-category and we prove that the fundamental group of this CW-complex is isomorphic to the intrinsic fundamental group of the k-category. This extends previous ...