The quadratic Poisson structures and related nonassociative noncommutative Zinbiel type algebras

Artemovych, O.D., Balinsky, Alexander ORCID: https://orcid.org/0000-0002-8151-4462 and Prykarpatski, A.K. 2019. The quadratic Poisson structures and related nonassociative noncommutative Zinbiel type algebras. Annals of Mathematics and Physics 2 (1) , 026-037. 10.17352/amp.000007

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Abstract

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

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Date of First Compliant Deposit:	17 December 2019
Date of Acceptance:	14 September 2019
Last Modified:	06 May 2023 02:14
URI:	https://orca.cardiff.ac.uk/id/eprint/127597

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