Author:
Artemovych Orest D.,Blackmore Denis,Prykarpatski Anatolij K.
Abstract
AbstractThere 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 of Balinsky–Novikov and Leibniz algebras are discussed. The non-associative structures of commutative algebras related with Balinsky–Novikov, Leibniz, Lie, and Zinbiel algebras are studied in detail.
Funder
Tadeusz Kosciuszko Cracow University of Technology
Publisher
Springer Science and Business Media LLC
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