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arXiv · 1304.3799

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

Jiwei He·Fred Van Oystaeyen·Yinhuo Zhang
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Abstract

Let $A$ be a Koszul Artin-Schelter regular algebra with Nakayama automorphism $ξ$. We show that the Yoneda Ext-algebra of the skew polynomial algebra $A[z;ξ]$ is a trivial extension of a Frobenius algebra. Then we prove that $A[z;ξ]$ 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 $A[z;ξ]$ 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.

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Jiwei He, Fred Van Oystaeyen, Yinhuo Zhang. 2013-06-10. Skew polynomial algebras with coefficients in Koszul Artin-Schelter regular algebras. https://arxiv.org/abs/1304.3799

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