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Simple algebras and exact module categories

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arxiv 2501.06629 v2 pith:M6SANJY7 submitted 2025-01-11 math.RT math.CTmath.QA

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keywords algebrafinitealgebrascategoriesexactjacobsonobjectradical
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Clifford and Weyl algebras in symmetric tensor categories

    math.RT 2026-07 accept novelty 8.0 of 10

    For a symplectic object V in a Frobenius exact symmetric tensor category with finite symmetric algebra, the Weyl algebra A(V) is Azumaya, and the resulting symplectic Witt group is described by Stiefel-Whitney classes...

  2. Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories

    math.QA 2025-06 accept novelty 8.0 of 10

    A finite braided tensor category is fully dualizable in the Morita 4-category of braided pre-tensor categories whenever its symmetric center is separable.

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