Non-homogeneous N-Koszul Algebras

this is a joint work with victor ginzburg [4] in which we study a class of associative algebras associated to finite groups acting on a vector space. these algebras are non-homogeneous n-koszul algebra generalizations of symplectic reflection algebras. we realize the extension of the n-koszul property to non-homogeneous algebras through a poincaré-birkhoff-witt property.