Abstract
An algebraic characterization of homogeneous quadratic Poisson structures is obtained and some methods to construct examples are given. A sufficient condition for the commutativity of a homogeneous quadratic Poisson structure and the Lie–Poisson structure on the dual of a Lie algebra is given. Quadratic Poisson structures on Lie algebras are discussed. A new Poisson structure is introduced and its application is shown.
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