Finite symmetric tensor categories with the Chevalley property in characteristic 2
Name
1904.07576.pdf
Description
Accepted version
Size
229.9 KB
Format
Adobe PDF
Checksum (MD5)
07b799cbb633fbe53f66293507fbe418
Author(s)
Etingof, Pavel
Gelaki, Shlomo
Date Issued
2021
Journal
Journal of Algebra and Its Applications
Publisher
World Scientific Pub Co Pte Lt
Version
Author's final manuscript
Abstract
We prove an analog of Deligne’s theorem for finite symmetric tensor categories [Formula: see text] with the Chevalley property over an algebraically closed field [Formula: see text] of characteristic [Formula: see text]. Namely, we prove that every such category [Formula: see text] admits a symmetric fiber functor to the symmetric tensor category [Formula: see text] of representations of the triangular Hopf algebra [Formula: see text]. Equivalently, we prove that there exists a unique finite group scheme [Formula: see text] in [Formula: see text] such that [Formula: see text] is symmetric tensor equivalent to [Formula: see text]. Finally, we compute the group [Formula: see text] of equivalence classes of twists for the group algebra [Formula: see text] of a finite abelian [Formula: see text]-group [Formula: see text] over an arbitrary field [Formula: see text] of characteristic [Formula: see text], and the Sweedler cohomology groups [Formula: see text], [Formula: see text], of the function algebra [Formula: see text] of [Formula: see text].
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1142/S0219498821400107
