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arXiv · 2501.06629

Simple algebras and exact module categories

Kevin Coulembier·Mateusz Stroiński·Tony Zorman
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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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Kevin Coulembier, Mateusz Stroiński, Tony Zorman. 2025-01-11. Simple algebras and exact module categories. https://arxiv.org/abs/2501.06629

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