1. Simple algebras and exact module categories
- Author
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Coulembier, Kevin, Stroiński, Mateusz, and Zorman, Tony
- Subjects
Mathematics - Representation Theory ,Mathematics - Category Theory ,Mathematics - Quantum Algebra ,18D25, 18M05 - 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., Comment: 25 pages, 18 figures; comments welcome!
- Published
- 2025