Translator Disclaimer
2022 Monoidal abelian envelopes and a conjecture of Benson and Etingof
Kevin Coulembier, Inna Entova-Aizenbud, Thorsten Heidersdorf
Algebra Number Theory 16(9): 2099-2117 (2022). DOI: 10.2140/ant.2022.16.2099

Abstract

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 SL2 in characteristic 2. We use our results on the abelian envelopes to prove this conjecture and its variants for any prime p.

Citation

Download Citation

Kevin Coulembier. Inna Entova-Aizenbud. Thorsten Heidersdorf. "Monoidal abelian envelopes and a conjecture of Benson and Etingof." Algebra Number Theory 16 (9) 2099 - 2117, 2022. https://doi.org/10.2140/ant.2022.16.2099

Information

Received: 11 December 2019; Revised: 15 July 2021; Accepted: 17 August 2021; Published: 2022
First available in Project Euclid: 18 January 2023

Digital Object Identifier: 10.2140/ant.2022.16.2099

Subjects:
Primary: 18D10
Secondary: 14L15 , 16D90

Keywords: abelian envelope , tensor category , tilting modules

Rights: Copyright © 2022 Mathematical Sciences Publishers

JOURNAL ARTICLE
19 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.16 • No. 9 • 2022
MSP
Back to Top