The quadratic Poisson structures and related nonassociative noncommutative Zinbiel type algebras

• Main Authors: Orest D Artemovych (Author), Alexandr Balinsky (Author), Anatolij K Prykarpatski (Author)
• פורמט: ספר
• יצא לאור: Annals of Mathematics and Physics - Peertechz Publications, 2019-09-16.
• נושאים: Research Article
• גישה מקוונת: Connect to this object online.

סיכום

<p>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.</p>

DOI

10.17352/amp.000007