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.
This is joint work with E. Herscovich (EPFL).
This video is part of the European Non-Associative Algebra Seminar series.
