HSE–Skoltech Laboratory of Representation Theory and Mathematical Physics seminar. Speaker: Abner Hernandez Rodriguez

Abstract:  We will discuss the structure of double Poisson brackets in the sense of M. Van den Bergh on finite-dimensional algebras. In particular (using Hochschild homology and some results) we prove that all possible double Poisson brackets on matrix algebras are given by inner derivations of appropriate type. As a corollary of this result, we see that all possible double Poisson brackets in any finite-dimensional semisimple algebra are also given by inner derivations. We further give a description of all double Poisson brackets on a small non-semisimple algebra (namely, the algebra of 2×2 upper triangular matrices); in addition, we discuss Poisson structures induced from the double Poisson brackets in its representation spaces of dimensions two and three.

P.S. Information about past seminars is available here: https://sites.google.com/site/alexandrburyakhomepage/lab-seminar?authuser=0