Non-associative structures of commutative algebras related with quadratic Poisson brackets
Authors:
- Orest D. Artemovych,
- Denis Blackmore,
- Anatolij K. Prykarpatski
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.
- Record ID
- CUT5499360ab4244d31911f1b2c6748979f
- Publication categories
- ;
- Author
- Journal series
- European Journal of Mathematics, ISSN 2199-675X, e-ISSN 2199-6768
- Issue year
- 2020
- Vol
- 6
- No
- 1
- Pages
- 208-231
- Other elements of collation
- Bibliografia (na s.) - 229-231; Bibliografia (liczba pozycji) - 51; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 6, Iss. 1, Spec. Iss.
- Substantive notes
- Special Issue: Mathematics in the Banach Space
- Keywords in English
- Balinsky-Novikov algebra, Lie algebra, Leibniz algebra, Zinbiel algebra, Derivation, Pre-Poisson brackets, Lie-Poisson structure
- DOI
- DOI:10.1007/s40879-020-00398-w Opening in a new tab
- URL
- https://link.springer.com/article/10.1007/s40879-020-00398-w Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 40
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT5499360ab4244d31911f1b2c6748979f/
- URN
urn:pkr-prod:CUT5499360ab4244d31911f1b2c6748979f
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.