Higher symplectic reflection algebras and non-homogeneous N-Koszul property

Symplectic reflection algebras and non-homogeneous N-Koszul property

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 ...

Koszul and Gorenstein properties for homogeneous algebras

Koszul property was generalized to homogeneous algebras of degree N > 2 in [5], and related to N -complexes in [7]. We show that if the N -homogeneous algebra A is generalized Koszul, AS-Gorenstein and of finite global dimension, then one can apply the Van den Bergh duality theorem [23] to A, i.e., there is a Poincaré duality between Hochschild homology and cohomology of A, as for N = 2. Mathem...

Continuous symplectic reflection algebras

The theory of PBW properties of quadratic algebras, to which this paper aims to be a modest contribution, originates from the pioneering work of Drinfeld (see [Dr1]). In particular, as we learned after publication of [EG] (to the embarrassment of two of us!), symplectic reflection algebras and even more general reflection algebras considered in Section 3.6 below, as well as PBW theorems for the...

Symplectic Reflection Algebras

We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, with category O, and with spaces of representations of quivers. Mathematics Subject Classification (2000). Primary 16G.

Symplectic Reflection Algebras