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

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

Research output: Contribution to journalArticlepeer-review

2 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 languageEnglish (US)
Pages (from-to)43-52
Number of pages10
JournalTopological Algebra and its Applications
Volume6
Issue number1
DOIs
StatePublished - Mar 1 2018

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Geometry and Topology
  • Algebra and Number Theory

Keywords

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

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