The Duflo-Serganova functor, vingt ans apr\`es
Maria Gorelik, Crystal Hoyt, Vera Serganova, Alexander Sherman
TL;DR
This paper reviews the Duflo-Serganova functor and associated varieties for Lie superalgebras, covering both historical results and recent developments, providing a comprehensive overview of this mathematical area.
Contribution
It consolidates original and recent results on the Duflo-Serganova functor and associated varieties, including proofs and survey of advancements in Lie superalgebra theory.
Findings
Reestablished original results and proofs from the unpublished manuscript
Summarized recent developments and applications of the Duflo-Serganova functor
Provided a comprehensive survey of the field
Abstract
We review old and new results concerning the functor and associated varieties for Lie superalgebras. These notions were introduced in the unpublished manuscript arXiv:math/0507198 by Michel Duflo and the third author. This paper includes the results and proofs of the original manuscript, as well as a survey of more recent results.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry