Title: Noncommutative algebraic structures

Speaker: Natalia Iyudu (University of Edinburgh)

Abstract: I will talk on one particular structure called pre-Calabi-Yau algebra. It was introduced around 2005 in attempt to describe a TQFT in case of open strings. This structure is essentially the Stasheff strong homotopy associative algebra on the A oplus A*, which is cyclic invariant w.r.t. natural inner form on A oplus A* solution of the Maurer-Cartan equation. It can be equivalently formulated in terms of higher Hochschild cohomology. We claim that pre-Calabi-Yau structure on an associative algebra A can be considered as a noncommutative Poisson structure on A. Noncommutative structure is understood as the one which induce corresponding conventional commutative structure on the representation spaces of A. I will describe the connection we found between a pre-Calabi-Yau structure and a double Poisson bracket introduced by Van den Bergh. The latter appears as a particular part of a pre-Calabi-Yau structure. If time permits I will touch upon some examples of calculation operadic homologies (homologies of trees).

Time: Thursday 20 June 2019, 2.30pm

Location: Lecture Room, 1st Floor, School of Theoretical Physics, DIAS, 10 Burlington Road, Dublin 4