تقرير
Monoidal abelian envelopes and a conjecture of Benson--Etingof
| العنوان: | Monoidal abelian envelopes and a conjecture of Benson--Etingof |
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| المؤلفون: | Coulembier, Kevin, Entova-Aizenbud, Inna, Heidersdorf, Thorsten |
| المصدر: | Alg. Number Th. 16 (2022) 2099-2117 |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Representation Theory, Mathematics - Category Theory |
| الوصف: | 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 $p$. Comment: ver 3: Generalized the results to arbitrary primes p (ver 1,2 dealt with the case p=2), ver 2: minor fix in the definition of abelian envelope |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.2140/ant.2022.16.2099 |
| URL الوصول: | http://arxiv.org/abs/1911.04303 |
| رقم الأكسشن: | edsarx.1911.04303 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.2140/ant.2022.16.2099 |
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