Open AccessThe quadratic Poisson structures and related nonassociative noncommutative Zinbiel type algebras
Author(s) -
Orest D. Artemovych,
Alexander Balinsky,
A. K. Prykarpatski
Publication year - 2019
Publication title -
annals of mathematics and physics
Language(s) - English
Resource type - Journals
ISSN - 2689-7636
DOI - 10.17352/amp.000007
Subject(s) - noncommutative geometry , poisson distribution , type (biology) , mathematics , quadratic equation , pure mathematics , algebra over a field , statistics , geology , geometry , paleontology
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.
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