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Monoidal abelian
envelopes and a conjecture of Benson and Etingof
Kevin Coulembier, Inna Entova-Aizenbud and Thorsten Heidersdorf |
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Vol. 16 (2022), No. 9, 2099–2117
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Abstract |
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We give several criteria to decide whether a given tensor category is the abelian envelope of a fixed symmetric monoidal category. As a main result we prove that the category of finite-dimensional representations of a semisimple simply connected algebraic group is the abelian envelope of the category of tilting modules. Benson and Etingof conjectured that a certain limit of finite symmetric tensor categories is tensor equivalent to the finite-dimensional representations of in characteristic . We use our results on the abelian envelopes to prove this conjecture and its variants for any prime . |
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Keywords
tensor category, tilting modules, abelian envelope
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Mathematical Subject Classification 2010
Primary: 18D10
Secondary: 14L15, 16D90
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Milestones
Received: 11 December 2019
Revised: 15 July 2021
Accepted: 17 August 2021
Published: 19 December 2022
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Authors |
| Kevin Coulembier | |
| School of Mathematics and
Statistics University of Sydney Australia |
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| Inna Entova-Aizenbud | |
| Department of Mathematics Ben Gurion University of the Negev Be’er-Sheva Israel |
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| Thorsten Heidersdorf | |
| Mathematisches Institut Universität Bonn Germany |
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