Noncommutative Poisson geometry and pre-Calabi-Yau algebras

Abstract: In order to define suitable noncommutative 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 noncommutative 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. This is a joint work with E. Herscovich (EPFL).

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar