Poisson brackets, Novikov-Leibniz structures and integrable Riemann hydrodynamic systems

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

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


A general differential-algebraic approach is devised for constructing multi-component Hamiltonian operators as differentiations on suitably constructed loop Lie algebras. The related Novikov-Leibniz algebraic structures are presented and a new non-associative “Riemann” algebra is constructed, which is closely related to the infinite multi-component Riemann integrable hierarchies. A close relationship to the standard symplectic analysis techniques is also discussed.

Original languageEnglish (US)
Pages (from-to)41-72
Number of pages32
JournalJournal of Nonlinear Mathematical Physics
Issue number1
StatePublished - Jan 2 2017

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • 2-cocycles
  • Hamiltonian operators
  • Novikov algebra
  • Poisson brackets
  • Riemann algebra
  • Riemann hydrodynamic hierarchy
  • differential algebras
  • differentiations
  • integrability
  • loop-algebra
  • right Leibniz algebra


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