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Monoidal abelian envelopes and a conjecture of Benson--Etingof by Coulembier, Kevin; Entova-Aizenbud, Inna; Heidersdorf, Thorsten is a scholarly article available to read on EtoBox.

What is Monoidal abelian envelopes and a conjecture of Benson--Etingof about?

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 $SL_2$ in characteristic $2$. We use our results on the abelian envelopes to prove this conjecture and its variants for any prime $p$.

Author

Coulembier, Kevin; Entova-Aizenbud, Inna; Heidersdorf, Thorsten

Published

2019

Language

EN