Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
Monoidal abelian envelopes and a conjecture of Benson and Etingof

### Kevin Coulembier, Inna Entova-Aizenbud and Thorsten Heidersdorf

Vol. 16 (2022), No. 9, 2099–2117
##### 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 ${\mathrm{SL}}_{2}$ in characteristic $2$. We use our results on the abelian envelopes to prove this conjecture and its variants for any prime $p$.

##### Keywords
tensor category, tilting modules, abelian envelope
##### Mathematical Subject Classification 2010
Primary: 18D10
Secondary: 14L15, 16D90