Symplectic reflection algebras and non-homogeneous N-Koszul property
نویسندگان
چکیده
From symplectic reflection algebras [12], some algebras are naturally introduced. We show that these algebras are non-homogeneous N Koszul algebras. The Koszul property was generalized to homogeneous algebras of degree N > 2 in [6]. In the present paper, the extension of the Koszul property to non-homogeneous algebras is realized through a PBW theorem. This PBW theorem is the generalization to the N -case of a quadratic result obtained by Braverman and Gaitsgory [11] (see also Polishchuk and Positselski [14]). Symplectic reflection algebras need to work over special non-commutative semi-simple rings. Actually, replacing the ground field by any von Neumann regular ring is more general and is well-adapted to the Koszul property and the PBW theorem.
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