Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-03-01
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| Series: | Topological Algebra and its Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/taa-2018-0005 |
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| author | Artemovych Orest D. Prykarpatski Anatolij K. Blackmore Denis L. |
| author_facet | Artemovych Orest D. Prykarpatski Anatolij K. Blackmore Denis L. |
| author_sort | Artemovych Orest D. |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-19T14:46:00Z |
| format | Article |
| id | doaj.art-2184b474e80c484abc92d46dfc2514fe |
| institution | Directory Open Access Journal |
| issn | 2299-3231 |
| language | English |
| last_indexed | 2024-12-19T14:46:00Z |
| publishDate | 2018-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Topological Algebra and its Applications |
| spelling | doaj.art-2184b474e80c484abc92d46dfc2514fe2022-12-21T20:16:57ZengDe GruyterTopological Algebra and its Applications2299-32312018-03-0161435210.1515/taa-2018-0005taa-2018-0005Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operatorsArtemovych Orest D.0Prykarpatski Anatolij K.1Blackmore Denis L.2Institute of Mathematics Cracow University of Technology, ul Warszawska 24, Kraków 31-155, PolandInstitute of Mathematics Cracow University of Technology, ul Warszawska 24, Kraków 31-155, PolandDepartment of Mathematical Sciences at NJIT, University Heights, Newark, NJ 07-102, USAWe 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.https://doi.org/10.1515/taa-2018-000517a3617d9917b40 |
| spellingShingle | Artemovych Orest D. Prykarpatski Anatolij K. Blackmore Denis L. Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators Topological Algebra and its Applications 17a36 17d99 17b40 |
| title | Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators |
| title_full | Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators |
| title_fullStr | Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators |
| title_full_unstemmed | Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators |
| title_short | Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators |
| title_sort | examples of lie and balinsky novikov algebras related to hamiltonian operators |
| topic | 17a36 17d99 17b40 |
| url | https://doi.org/10.1515/taa-2018-0005 |
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