Séminaire Algèbre ICJ
# Exposé d'Estanislao Herscovich (Grenoble): Double quasi-Poisson algebras are pre-Calabi-Yau

→
Europe/Paris

en ligne (https://webconf.lal.cloud.math.cnrs.fr/b/flo-k3r-y9a)
### en ligne

#### https://webconf.lal.cloud.math.cnrs.fr/b/flo-k3r-y9a

https://webconf.lal.cloud.math.cnrs.fr/b/flo-k3r-y9a

Description

Double Poisson and double quasi-Poisson algebras were introduced by M. Van den Bergh in his study of noncommutative quasi-Poisson geometry. Namely, they satisfy the so-called Kontsevich-Rosenberg principle, since the representation scheme of a double (quasi-)Poisson algebras has a natural (quasi-)Poisson structure. On the other hand, N. Iyudu and M. Kontsevich found a link between double Poisson algebras and pre-Calabi-Yau algebras, a notion introduced by Kontsevich and Y. Vlassopoulos. The aim of this talk will be to explain how such connection can be extended to double quasi-Poisson algebras, which thus give rise to pre-Calabi-Yau algebras. This pre-Calabi-Yau structure is however more involved in the case of double quasi-Poisson algebras since, in particular, we get an infinite number of nonvanishing higher multiplications for the associated pre-Calabi-Yau algebra, which involve the Bernoulli numbers.

This is a joint work with D. Fernández from the Universität Bielefeld.