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

Orest D. Artemovych; Anatolij K. Prykarpatski; Denis L. Blackmore

doi:10.1515/taa-2018-0005

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

Orest D. Artemovych, Anatolij K. Prykarpatski, Denis L. Blackmore

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English (US)
Pages (from-to)	43-52
Number of pages	10
Journal	Topological Algebra and its Applications
Volume	6
Issue number	1
DOIs	https://doi.org/10.1515/taa-2018-0005
State	Published - Mar 1 2018

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology
Applied Mathematics

Keywords

Balinsky-Novikov algebra
Brane algebra
Derivation
Endomorphism
Lie algebra
Lie-Poisson structure
Pre-Poisson brackets
Torus-algebra

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title = "Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators",

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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AU - Artemovych, Orest D.

AU - Prykarpatski, Anatolij K.

AU - Blackmore, Denis L.

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N2 - 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.

AB - 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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KW - Brane algebra

KW - Derivation

KW - Endomorphism

KW - Lie algebra

KW - Lie-Poisson structure

KW - Pre-Poisson brackets

KW - Torus-algebra

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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