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 |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 2299-3231 |