Quadratic Poisson brackets compatible with an algebra structure
arXiv:hep-th/9407041 · doi:10.1088/0305-4470/27/18/008
Abstract
Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among compatible brackets, a subclass of coboundary brackets is described, and such brackets are enumerated in a number of examples.
6 pages