Skew Calabi-Yau algebras are generalizations of Calabi-Yau algebras due to Reyes, Rogalski, and Zhang. Within the graded (associative and unital) algebras over a field k, they form the non-commutative analogues of the regular algebras. As a special feature, such an algebra A is equipped with its so-called Nakayama automorphism φ. The talk will present ongoing investigations on the presentations of these algebras by generators and relations taking into account their homological specificities. Such presentations are well-known for Calabi-Yau algebras (after Ginzburg, Bocklandt and van den Bergh) and also for Koszul skew Calabi-Yau algebras (after Bocklandt, Wemyss and Schedler). The general situation involves the interaction of the A∞-Yoneda algebra E(A) := ExtA(k,k) with the Nakayama automorphism φ, and also the A∞-Yoneda algebra E(A[x,φ]) of the Ore extension A[x,φ] of A by φ. More precisely, one is particularly intereseted in minimal models of these A∞-algebras. After having presented all these concepts, I will discuss the relationship between these minimal models as well as consequences in terms of presentations of A.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
