A transposed Poisson algebra is a triple (L,⋅,[⋅,⋅]) consisting of a vector space L with two bilinear operations ⋅ and [⋅,⋅], such that (L,⋅) is a commutative associative algebra; (L,[⋅,⋅]) is a Lie algebra; and the ‘transposed’ Leibniz law holds: 2z⋅[x,y]=[z⋅x,y]+[x,z⋅y] for all x,y,z∈L. A transposed Poisson algebra structure on a Lie algebra (L,[⋅,⋅]) is a (commutative associative) multiplication ⋅ on L such that (L,⋅,[⋅,⋅]) is a transposed Poisson algebra. I will give an overview of my recent results in collaboration with Ivan Kaygorodov (Universidade da Beira Interior) on the classification of transposed Poisson structures on several classes of Lie algebras.
This video is part of the European Non-Associative Algebra Seminar series.
