Classification of simple algebras in Deligne category $Rep(S_t)$
Nate Harman, Daniil Kalinov
TL;DR
This paper classifies simple associative and Lie algebras within Deligne categories $Rep(S_t)$, providing a comprehensive answer to a question posed by Etingof about their structure.
Contribution
It offers the first complete classification of simple algebras in Deligne categories, expanding understanding of their algebraic structures.
Findings
Complete classification of simple associative algebras in $Rep(S_t)$
Complete classification of simple Lie algebras in $Rep(S_t)$
Addresses and resolves Etingof's open question
Abstract
We classify simple associative and Lie algebras inside the Deligne categories , answering a question posed by Etingof.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology