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.