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

Authors
  • Artemovych, Orest D.
  • Prykarpatski, Anatolij K.
  • Blackmore, Denis L.
Type
Published Article
Journal
Topological Algebra and its Applications
Publisher
De Gruyter Open
Publication Date
Mar 28, 2018
Volume
6
Issue
1
Pages
43–52
Identifiers
DOI: 10.1515/taa-2018-0005
Source
De Gruyter
Keywords
License
Green

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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