no. 3
On the representation type of a finite tensor category
Bergh, Petter Andreas1 ; Erdmann, Karin2; Plavnik, Julia Yael3, 4 orcid; Witherspoon, Sarah J.5 orcid
1Institutt for matematiske fag, NTNU, N-7491 Trondheim, Norway
2Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Oxford OX2 6GG, United Kingdom
3Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USA
4Department of Mathematics and Data Science, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
5Department of Mathematics, Texas A & M University, College Station, Texas 77843, USA
Annals of Representation Theory, Volume 3 (2026) no. 3, pp. 565-578

Given an exact module category over a finite tensor category with finitely generated cohomology, we show that if there exists an object of complexity at least three, then the category is of wild representation type. In particular, if the Krull dimension of the cohomology ring of the finite tensor category is at least three, then this category is wild.

Received:
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Accepted:
Published online:
DOI: 10.5802/art.50
Classification: 16G60, 16T05, 18M05, 18M15
Keywords: finite tensor categories, representation type

Bergh, Petter Andreas  1 ; Erdmann, Karin  2 ; Plavnik, Julia Yael  3 , 4 ; Witherspoon, Sarah J.  5

1 Institutt for matematiske fag, NTNU, N-7491 Trondheim, Norway
2 Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Oxford OX2 6GG, United Kingdom
3 Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USA
4 Department of Mathematics and Data Science, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
5 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
Bergh, Petter Andreas; Erdmann, Karin; Plavnik, Julia Yael; Witherspoon, Sarah J. On the representation type of a finite tensor category. Annals of Representation Theory, Volume 3 (2026) no. 3, pp. 565-578. doi: 10.5802/art.50
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