PBW-deformations of N-Koszul algebras

For a quotient algebra U of the tensor algebra we give explicit conditions on its relations for U being a PBW-deformation of an N-Koszul algebra A. We show that there is a one-to-one correspondence between such deformations and a class of A∞-structures on the Yoneda algebra of A. We compute the PBW-deformations of the algebra whose relations are the anti-symmetrizers of degree N and also of cubic Artin–Schelter algebras.