On symmetric fusion categories in positive characteristic

By V. Ostrik. Selecta Mathematica, 2015

53 citations recorded by the source corpus.

We propose a conjectural extension in the positive characteristic case of well known Deligne’s theorem on the existence of super fiber functors. We prove our conjecture in the special case of semisimple categories with finitely many isomorphism classes of simple objects.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/365d8e6e07363f2998f67aa807decc30420549eb

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In Algebra and Number Theory

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

On semisimplification of tensor categories (2018, background): “ Rep kG= Rep kL. So let us consider the case p>2 and compute the category (Verp)L more explicitly. Note that Verp = Ver + p ⊠Supervec, and Verp has no nontrivial symmetric tensor autoequivalences ([O]), while Ver+ p has no nontrivial tensor automorphisms of the identity functor. Thus, from Coroll”
On the Classification of Topological Orders (2020, background): “With the word “separable” added everywhere to the phrase “symmetric multifusion category,” Theorem 7 remains true in positive characteristic, and is due to [Ost15], and so a version of Theorem 8 below applies in all characteristics.”