Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators
Authors:
- Orest D. Artemovych,
- Anatolij K. Prykarpatski,
- Denis L. Blackmore
Abstract
We study algebraic properties of Poisson brackets on non-associative non-commutative algebras, compatible with their multiplicative structure. Special attention is paid to the Poisson brackets of the Lie-Poisson type, related with the special Lie-structures on the differential-topological torus and brane algebras, generalizing those studied before by Novikov-Balinsky and Gelfand-Dorfman. Illustrative examples of Lie and Balinsky-Novikov algebras are discussed in detail. The non-associative structures (induced by derivation and endomorphism) of commutative algebras related to Lie and Balinsky-Novikov algebras are described in depth.
- Record ID
- CUTedfecc0273ce400280d5731d260222bc
- Publication categories
- ;
- Author
- Journal series
- Topological Algebra and its Applications, ISSN , e-ISSN 2299-3231
- Issue year
- 2018
- Vol
- 6
- No
- 1
- Pages
- 43-52
- Other elements of collation
- Bibliografia (na s.) - 52; Bibliografia (liczba pozycji) - 23; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 6, Iss. 1
- Keywords in English
- pre-Poisson brackets, Lie-Poisson structure, Balinsky-Novikov algebra, Lie algebra, brane algebra, torus-algebra, derivation, endomorphism
- DOI
- DOI:10.1515/taa-2018-0005 Opening in a new tab
- URL
- https://www.degruyter.com/view/j/taa.2018.6.issue-1/taa-2018-0005/taa-2018-0005.xml Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 1
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTedfecc0273ce400280d5731d260222bc/
- URN
urn:pkr-prod:CUTedfecc0273ce400280d5731d260222bc
* 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.