PBW-deformations of N-Koszul algebras

Abstract

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 there is a one-one correspondence between such deformations and a class of $A_{\infty }$-structures on the Yoneda algebra $Ex{t}_A^{\ast }(k,k)$ 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.

35 pages. Some minor corrections

References in corpus (2)

• Nonhomogeneous quadratic duality and curvature
• Symplectic reflection algebras and non-homogeneous N-Koszul property

Cited by in corpus (13)

• Gerasimov's theorem and N-Koszul algebras
• Note on Nakayama automorphisms of PBW deformations and Hopf actions
• Deformations of Koszul Artin-Schelter Gorenstein algebras
• Poincare-Birkhoff-Witt Theorems
• Artin-Schelter regular algebras of dimension five
• PBW deformations of a Fomin-Kirillov algebra and other examples
• Quotients of Koszul algebras with almost linear resolution
• Deformations of path algebras of quivers with relations
• Poincare-Birkhoff-Witt Deformations of Calabi-Yau Algebras
• A${}_{\infty }$ deformations of extended Khovanov arc algebras and Stroppel's conjecture
• PBW-deformations of smash products involving Hopf algebra of Kac-Paljutkin type
• Non-Commutative Formal Groups In Positive Characterstic
• The General PBW Property