Annals of Mathematics and Physics


    Open Access Research Article Article ID: AMP-2-107

    The quadratic Poisson structures and related nonassociative noncommutative Zinbiel type algebras

    Orest D Artemovych, Alexandr Balinsky and Anatolij K Prykarpatski*

    There are studied algebraic properties of the quadratic Poisson brackets on nonassociative noncommutive algebras, compatible with their multiplicative structure. Their relations both with differentiations of the symmetric tensor algebras and Yang-Baxter structures on the adjacent Lie algebras are demonstrated. Special attention is payed to the quadtatic Poisson brackets of the Lie-Poisson type, the examples of the Novikov and Leibniz algebras are discused. The nonassociated structures of commutative algebras related with Novikov, Leibniz, Lie and Zinbiel algebras are studied in details.


    Published on: Sep 16, 2019 Pages: 26-37

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