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
Leave a Comment
Last Updated: 18th June 2019 by George Rogers
Thursday 20th June : STP Seminar – Noncommutative algebraic structures
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
Category: Regular seminars, School of Theoretical Physics News & Events
Recent Posts
Irish scientists are part of groundbreaking discovery with James Webb Space Telescope
Dr Pauline Gagnon (formerly of CERN) to deliver two talks at DIAS
DIAS Professor announced as next President of the European Southern Observatory’s Council
Quake Shake: New programme encourages people to get involved in monitoring earthquakes
DIAS announces programme for Samhain agus Science festival 2023
Language switcher