Non-associative structures of commutative algebras related with quadratic Poisson brackets

Authors

Orest D. Artemovych, Politechnika Krakowska
Denis Blackmore, New Jersey Institute of Technology
Anatolij K. Prykarpatski, Politechnika Krakowska

Document Type

Article

Publication Date

3-1-2020

Abstract

There 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.

Identifier

85079436164 (Scopus)

Publication Title

European Journal of Mathematics

External Full Text Location

https://doi.org/10.1007/s40879-020-00398-w

e-ISSN

21996768

ISSN

2199675X

First Page

208

Last Page

231

Issue

1

Volume

6

Recommended Citation

Artemovych, Orest D.; Blackmore, Denis; and Prykarpatski, Anatolij K., "Non-associative structures of commutative algebras related with quadratic Poisson brackets" (2020). Faculty Publications. 5424.
https://digitalcommons.njit.edu/fac_pubs/5424