On the representation type of a finite tensor category

2025/09/25 by Bergh, Petter Andreas, Erdmann, Karin, Plavnik, Julia Yael +1
#16G60 #16T05 #18M05 #18M15 #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2509.20853

Abstract

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.

Citations

• Support varieties without the tensor product property
• Support varieties for finite tensor categories: the tensor product property
• Incompressible tensor categories
• On cohomology in symmetric tensor categories in prime characteristic
• New incompressible symmetric tensor categories in positive characteristic
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• Relative support varieties

Related

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• Finite tensor categories
• A Finite-Tame-Wild Trichotomy Theorem for Tensor Diagrams
• Separable equivalences, finitely generated cohomology and finite tensor categories
• Module categories over equivariantized tensor categories