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Article Dans Une Revue International Mathematics Research Notices Année : 2011

Deformations of Orbifolds with Noncommutative Linear Poisson Structures

Résumé

Let Γ be a finite group acting faithfully and linearly on a real 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^∗) ⋊ Γ. We prove that the quotient algebras of T(V^∗) ⋊ Γ by such relations satisfy the Poincaré-Birkhoff-Witt (PBW) property. Such quotient algebras can be viewed as quantizations of linear or constant Poisson structures on T(V^∗) ⋊ Γ, and are natural generalizations of symplectic reflection algebras. We study these algebras via various examples and their related cohomologies.
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Dates et versions

hal-00802505 , version 1 (20-03-2013)

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Jean-Michel Oudom, Gilles Halbout, Xiang Tang. Deformations of Orbifolds with Noncommutative Linear Poisson Structures. International Mathematics Research Notices, 2011, 2011 (1), pp.1-39. ⟨10.1093/imrn/rnq065⟩. ⟨hal-00802505⟩
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