Support varieties for finite tensor categories: the tensor product property
Bergh, Petter Andreas1; Plavnik, Julia Yael2; Witherspoon, Sarah3
1 Institutt for matematiske fag, NTNU, N-7491 Trondheim, Norway
2 Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USA
3 Department of Mathematics, Texas A & M University, College Station, Texas 77843, USA
Annals of Representation Theory, Volume 1 (2024) no. 4, pp. 539-566.

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.

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DOI: 10.5802/art.18
Classification: 16E40, 16T05, 18M05, 18M15
Keywords: finite tensor categories, support varieties, tensor product property
Bergh, Petter Andreas 1; Plavnik, Julia Yael 2; Witherspoon, Sarah 3

1 Institutt for matematiske fag, NTNU, N-7491 Trondheim, Norway
2 Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USA
3 Department of Mathematics, Texas A & M University, College Station, Texas 77843, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Bergh, Petter Andreas; Plavnik, Julia Yael; Witherspoon, Sarah. Support varieties for finite tensor categories: the tensor product property. Annals of Representation Theory, Volume 1 (2024) no. 4, pp. 539-566. doi : 10.5802/art.18. https://art.centre-mersenne.org/articles/10.5802/art.18/

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