Cleft extensions of Koszul twisted Calabi-Yau algebras

الأصل · EN

Let H be a twisted Calabi-Yau (CY) algebra and σ a 2-cocycle on H. Let A be an N-Koszul twisted CY algebra such that A is a graded Hσ-module algebra. We show that the cleft extension A#σH is also a twisted CY algebra. This result has two consequences. Firstly, the smash product of an N-Koszul twisted CY algebra with a twisted CY Hopf algebra is still a twisted CY algebra. Secondly, the cleft objects of a twisted CY Hopf algebra are all twisted CY algebras. As an application of this property, we determine which cleft objects of U(D,λ), a class of pointed Hopf algebras introduced by Andruskiewitsch and Schneider, are Calabi-Yau algebras.