Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators

Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators AbstractWe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Topological Algebra and its Applications de Gruyter

Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators

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Publisher
De Gruyter Open
Copyright
© 2018
ISSN
2299-3231
eISSN
2299-3231
D.O.I.
10.1515/taa-2018-0005
Publisher site
See Article on Publisher Site

Abstract

AbstractWe 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.

Journal

Topological Algebra and its Applicationsde Gruyter

Published: Mar 28, 2018

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