Poisson structures on (non)associative noncommutative algebras and integrable Kontsevich type Hamiltonian systems - Oksana E Hentosh; Alexander A Balinsky; Anatolij K Prykarpatski (Annals of Mathematics and Physics - Peertechz Publications, 2020)
We have revisited the classical Poisson manifold approach, closely related to construction of Hamiltonian operators, generated by nonassociative and noncommutative algebras. In particular, we presented its natural and simple generalization allowing effectively to describe a wide class of Lax type integrable nonlinear Kontsevich type Hamiltonian systems on associative noncommutative algebras.