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

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 ˆw is also constructed so that the Calabi–Yau algebra A[z; ξ ] is isomorphic to the derivation quotient of ˆw . 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.

Jaar van publicatie:2013

Trefwoorden:Koszul Artin–Schelter regular algebra Skew polynomial algebra Calabi–Yau algebra Superpotential PBW-deformation

BOF-keylabel:ja

IOF-keylabel:ja

BOF-publication weight:1

CSS-citation score:1

Auteurs:International

Authors from:Higher Education

Toegankelijkheid:Closed