Semisimple and G-Equivariant Simple Algebras Over Operads
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10485_2016_Article_9435.pdf
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Author(s)
Etingof, Pavel
Date Issued
April 2016
Journal
Applied Categorical Structures
Publisher
Springer Netherlands
Citation
Etingof, Pavel. “Semisimple and G-Equivariant Simple Algebras Over Operads.” Applied Categorical Structures (April 20, 2016).
Version
Author's final manuscript
Abstract
Let G be a finite group. There is a standard theorem on the classification of G-equivariant finite dimensional simple commutative, associative, and Lie algebras (i.e., simple algebras of these types in the category of representations of G). Namely, such an algebra is of the form A=Fun[subscript H](G,B), where H is a subgroup of G, and B is a simple algebra of the corresponding type with an H-action. We explain that such a result holds in the generality of algebras over a linear operad. This allows one to extend Theorem 5.5 of Sciarappa (arXiv:1506.07565) on the classification of simple commutative algebras in the Deligne category Rep(S[subscript t]) to algebras over any finitely generated linear operad.
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/10.1007/s10485-016-9435-1
