Deformations of linear Poisson orbifolds

Details Deformations of linear Poisson orbifolds Deformations of linear Poisson orbifolds

2008-06-30

arxiv.org/abs/0807.0027v1

Mathematics

Quantum Algebra

23 pages

Scientific paper

Let $\Gamma$ 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 $\Gamma$ action. We study generalized quadratic relations on the tensor algebra $T(V)\rtimes \Gamma$. We prove that the quotient algebras of $T(V)\rtimes \Gamma$ by such relations satisfy PBW property. Such quotient algebras can be viewed as quantizations of linear or constant Poisson structures on $S(V)\rtimes \Gamma$, and are natural generalizations of symplectic reflection algebras.

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