Seminario Geometría

Noncommutative Poisson geometry and pre-Calabi-Yau algebras

Ponente:  David Fernández (Luxembourg University)
Fecha:  jueves 29 de junio de 2023 - 12:00
Lugar:  Aula Gris 1, ICMAT


A long-standing problem in Poisson geometry has been the definition of suitable 'noncommutative Poisson structures'. To solve it, M. Van den Bergh introduced double Poisson algebras and double quasi-Poisson algebras, which can be regarded as noncommutative analogues of the usual Poisson and quasi-Poisson manifolds, respectively. N. Iyudu and M. Kontsevich found an insightful correspondence between double Poisson algebras and pre-Calabi-Yau algebras; certain cyclic A_\infty-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. Interestingly, they involve an infinite number of non-vanishing higher multiplications weighted by the Bernoulli numbers. This is a joint work with E. Herscovich (Grenoble).