Double (quasi-)Poisson algebras and their morphisms
Maxime Fairon (University of Glasgow)
Wednesday 25th November, 2020 16:00-17:00 zoom (online)
The talk will begin with a review of the notion of double (quasi-)Poisson algebras, which were introduced by Van den Bergh as noncommutative analogues of (quasi-)Poisson algebras. I will then explain how their morphisms can be used to understand morphisms of associated Poisson varieties. As an application, I will describe how the double (quasi-)Poisson algebra associated to an arbitrary quiver by Van den Bergh does not depend on the orientation of the quiver, up to isomorphism. We will see that this produces many Poisson isomorphisms between (multiplicative) quiver varieties. This is partly based on arXiv:2008.01409.