Work

Support varieties for finite tensor categories: the tensor product property

Year: 2024

Type: article

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 result to deduce the tensor product property for a large class of categories, those of modules for skew group algebras formed by exterior algebras with certain finite group actions. These include the symmetric finite tensor categories over algebraically closed fields of characteristic zero, thus giving a new proof of the tensor product property for these categories.

Source: Annals of representation theory

DOI: 10.5802/art.18

Authors: Petter Andreas Bergh, Julia Yael Plavnik, Sarah Witherspoon

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4404106111

FWCI: 1.346

Cites: 33

Cited by: 2

Related to: 10