The notion of a double Poisson bracket on an associative algebra was introduced by M. Van den Bergh in order to induce a (usual) Poisson bracket on the representation spaces of this algebra. I will start by reviewing the basics of this theory and its relation to other interesting operations, such as Leibniz brackets and H0-Poisson structures. I will then explain some recent results and generalisations related to double Poisson brackets.
This video is part of the European Non-Associative Algebra Seminar series.
