Simple algebras and exact module categories
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917898171187200 |
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| author | Coulembier, Kevin Stroiński, Mateusz Zorman, Tony |
| author_facet | Coulembier, Kevin Stroiński, Mateusz Zorman, Tony |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simple algebras and exact module categories Coulembier, Kevin Stroiński, Mateusz Zorman, Tony Representation Theory Category Theory Quantum Algebra 18D25, 18M05 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. |
| title | Simple algebras and exact module categories |
| topic | Representation Theory Category Theory Quantum Algebra 18D25, 18M05 |
| url | https://arxiv.org/abs/2501.06629 |