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Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators by Artemovych, Orest D.; Prykarpatski, Anatolij K.; Blackmore, Denis L. is a Mathematics article available to read on EtoBox.
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## 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.
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It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Artemovych, Orest D.; Prykarpatski, Anatolij K.; Blackmore, Denis L.
- Publisher
- De Gruyter Open Sp. z o.o. ; Warsaw: De Gruyter Open; Walter de Gruyter GmbH (ISSN 2299-3231)
- Published
- 2018
- Language
- EN
- Field
- Mathematics (Physical Sciences)
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