Deformations of linear Poisson orbifolds

2008/06/30 by Gilles Halbout, Halbout, Gilles, Jean-Michel Oudom +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.QA #math.RA

paper · pdf · doi:10.48550/arxiv.0807.0027

23 pages

arxiv created 2008/06/30 · arxiv updated 2009/12/01

Abstract

Let Γ be a finite group acting faithfully and linearly on a vector space V. Let T(V) (S(V)) be the tensor (symmetric) algebra associated to V which has a natural Γ action. We study generalized quadratic relations on the tensor algebra T(V)\rtimes Γ. We prove that the quotient algebras of T(V)\rtimes Γ by such relations satisfy PBW property. Such quotient algebras can be viewed as quantizations of linear or constant Poisson structures on S(V)\rtimes Γ, and are natural generalizations of symplectic reflection algebras.

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