New Constructions of Exceptional Simple Lie Superalgebras with Integer Cartan Matrix in Characteristics 3 and 5 via Tensor Categories
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31_2022_Article_9751.pdf
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1.3 MB
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Checksum (MD5)
3667b9e19cc08c51df4e9da3127a53d5
Author(s)
Kannan, Arun S.
Date Issued
August 17, 2022
Publisher
Springer US
Citation
Kannan, Arun S. 2022. "New Constructions of Exceptional Simple Lie Superalgebras with Integer Cartan Matrix in Characteristics 3 and 5 via Tensor Categories."
Version
Final published version
Abstract
Abstract
Using tensor categories, we present new constructions of several of the exceptional simple Lie superalgebras with integer Cartan matrix in characteristic p = 3 and p = 5 from the complete classification of modular Lie superalgebras with indecomposable Cartan matrix and their simple subquotients over algebraically closed fields by Bouarroudj, Grozman, and Leites in 2009. Specifically, let αp denote the kernel of the Frobenius endomorphism on the additive group scheme
G
a
$\mathbb {G}_{a}$
over an algebraically closed field of characteristic p. The Verlinde category Verp is the semisimplification of the representation category Repαp, and Verp contains the category of super vector spaces as a full subcategory. Each exceptional Lie superalgebra we construct is realized as the image of an exceptional Lie algebra equipped with a nilpotent derivation of order at most p under the semisimplification functor from Repαp to Verp.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00031-022-09751-7
