Solvability of a class of braided fusion categories

We show that a weakly integral braided fusion category C such that every simple object of C has Frobenius-Perron dimension at most 2 is solvable. In addition, we prove that such a fusion category is group-theoretical in the extreme case where the universal grading group of C is trivial.Comment: 12 pages, amslate

On fusion categories with few irreducible degrees

We prove some results on the structure of certain classes of integral fusion categories and semisimple Hopf algebras under restrictions on the set of their irreducible degrees.Fil: Natale, Sonia Lujan. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Plavnik, Julia Yael. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Support varieties for finite tensor categories: the tensor product property

We show that in a finite tensor category, the tensor product property holds for support varieties if and only if it holds between indecomposable periodic objects. We apply this to certain Hopf algebras in the form of skew group algebras. In particular, we show that the tensor product property holds for all objects in a symmetric finite tensor category over an algebraically closed field of characteristic zero.Comment: 29 page