Support varieties for finite tensor categories: the tensor product property

Abstract

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.

29 pages