Deformations of linear Poisson orbifolds
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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.
23 pages
23 pages