English

Support varieties for finite tensor categories: the tensor product property

Quantum Algebra 2024-06-07 v3 K-Theory and Homology Representation Theory

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.

Keywords

Cite

@article{arxiv.2306.16082,
  title  = {Support varieties for finite tensor categories: the tensor product property},
  author = {Petter Andreas Bergh and Julia Yael Plavnik and Sarah Witherspoon},
  journal= {arXiv preprint arXiv:2306.16082},
  year   = {2024}
}

Comments

29 pages

R2 v1 2026-06-28T11:16:37.543Z