Tag - Calabi-Yau algebras

David Fernández: Non-commutative Poisson geometry and pre-Calabi-Yau algebras

2nd December, 2024

In order to define suitable non-commutative Poisson structures, M. Van den Bergh introduced double Poisson algebras and double quasi-Poisson algebras. Furthermore, N. Iyudu and M. Kontsevich found an insightful correspondence between double Poisson algebras and pre-Calabi-Yau algebras; certain cyclic A∞-algebras which can be seen as non-commutative versions of shifted Poisson manifolds. In this talk, I will present an extension of the Iyudu-Kontsevich correspondence to the differential graded setting. I will also explain how double quasi-Poisson algebras give rise to pre-Calabi-Yau algebras.

Patrick Le Meur: Equivariant models for graded algebras and application to Calabi-Yau duality

16th July, 2020

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.