Simple algebras and exact module categories

2025/01/11 by Kevin Coulembier, Coulembier, Kevin, Mateusz Stroiński +3
Mathematics · #18D25 #18M05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2501.06629

openalex publication_date 2025/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We verify a conjecture of Etingof and Ostrik, stating that an algebra object in a finite tensor category is exact if and only if it is a finite direct product of simple algebras. Towards that end, we introduce an analogue of the Jacobson radical of an algebra object, similar to the Jacobson radical of a finite-dimensional algebra. We give applications of our main results in the context of incompressible finite symmetric tensor categories.

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• Relatively divisible and relatively flat objects in exact categories:\n Applications
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