Skew polynomial algebras with coefficients in Koszul Artin-Schelter regular algebras

Abstract

Let $A$ be a Koszul Artin-Schelter regular algebra with Nakayama automorphism $\xi$. We show that the Yoneda Ext-algebra of the skew polynomial algebra $A[z;\xi ]$ is a trivial extension of a Frobenius algebra. Then we prove that $A[z;\xi ]$ is Calabi-Yau; and hence each Koszul Artin Schelter regular algebra is a subalgebra of a Koszul Calabi-Yau algebra. A superpotential $\hat{w}$ is also constructed so that the Calabi-Yau algebra $A[z;\xi ]$ is isomorphic to the derivation quotient of $\hat{w}$. The Calabi-Yau property of a skew polynomial algebra with coefficients in a PBW-deformation of a Koszul Artin-Schelter regular algebra is also discussed.

minor corrections made, to appear in Journal of Algebra

References in corpus (4)

• Calabi-Yau algebras
• Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence
• Deformations of Koszul Artin-Schelter Gorenstein algebras
• Hopf algebra actions on differential graded algebras and applications

Cited by in corpus (2)

• Note on Nakayama automorphisms of PBW deformations and Hopf actions
• Deformations of Koszul Artin-Schelter Gorenstein algebras