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.
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}
}
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29 pages