Simple algebras and exact module categories
Representation Theory
2025-01-22 v2 Category Theory
Quantum Algebra
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.
Cite
@article{arxiv.2501.06629,
title = {Simple algebras and exact module categories},
author = {Kevin Coulembier and Mateusz Stroiński and Tony Zorman},
journal= {arXiv preprint arXiv:2501.06629},
year = {2025}
}
Comments
25 pages, 18 figures; comments welcome!