Finite W-superalgebras for queer Lie superalgebras

2010/12/10 by Lei Zhao, Zhao, Lei · 2 citations
Mathematics · #17B20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:17B20

paper · pdf · doi:10.48550/arxiv.1012.2326

The original submission was broken into two parts. This is the first part; the second part will posted later

openalex publication_date 2010/12/10 · arxiv created 2012/05/07 · arxiv updated 2012/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We initiate and develop the theory of finite W-superalgebras W_χ associated to the queer Lie superalgebra \g=\q(N) and a nilpotent linear functional χ∈ \ev\g^*. We show that the definition of the W-superalgebra is independent of various choices. We also establish a Skryabin type equivalence between the category of W_χ-modules and a category of certain \g-modules.

Cited by

• Dimensions of irreducible modules over W-algebras and Goldie ranks
• On Kostant's theorem for the Lie superalgebra Q(n)

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