Symmetric tensor categories in characteristic 2

Abstract

We construct and study a nested sequence of finite symmetric tensor categories Vec=C0⊂C1⊂⋯⊂Cn⊂⋯ over a field of characteristic 2 such that C2n are incompressible, i.e., do not admit tensor functors into tensor categories of smaller Frobenius–Perron dimension. This generalizes the category C1 described by Venkatesh [28] and the category C2 defined by Ostrik. The Grothendieck rings of the categories C2n and C2n+1 are both isomorphic to the ring of real cyclotomic integers defined by a primitive 2n+2-th root of unity, On=Z[2cos⁡(π/2n+1)].