Non-associative structures of commutative algebras related with quadratic Poisson brackets
Non-associative structures of commutative algebras related with quadratic Poisson brackets
Abstract There are studied algebraic properties of quadratic Poisson brackets on non-associative non-commutative algebras, compatible with their multiplicative structure. Their relations both with derivations of symmetric tensor algebras and Yang–Baxter structures on the adjacent Lie algebras are demonstrated. Special attention is paid to quadratic Poisson brackets of Lie–Poisson type, examples …