Non-associative structures of commutative algebras related with quadratic Poisson brackets

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

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2 Scopus citations


There are studied algebraic properties of quadratic Poisson brackets on non-associative non-commutative algebras, compatible with their multiplicative structure. Their relations both with derivations of symmetric tensor algebras and Yang–Baxter structures on the adjacent Lie algebras are demonstrated. Special attention is paid to quadratic Poisson brackets of Lie–Poisson type, examples of Balinsky–Novikov and Leibniz algebras are discussed. The non-associative structures of commutative algebras related with Balinsky–Novikov, Leibniz, Lie, and Zinbiel algebras are studied in detail.

Original languageEnglish (US)
Pages (from-to)208-231
Number of pages24
JournalEuropean Journal of Mathematics
Issue number1
StatePublished - Mar 1 2020

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Balinsky–Novikov algebra
  • Derivation
  • Leibniz algebra
  • Lie algebra
  • Lie–Poisson structure
  • Pre-Poisson brackets
  • Zinbiel algebra


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