The higher order Hamiltonian structures for the modified classical Yang-Baxter equation

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Abstract

We consider constructing the higher order Hamiltonian structures on the dual of the Lie algebra from the first Hamiltonian structure of the coadjoint orbit method. For this purpose we show that the structure of the Lie algebra g is inherited to the algebra of vector fields on g* through the solution of the Modified Classical Yang-Baxter equation (Classical r matrix). We study the algebra that generates the compatible Poisson brackets.

Original languageEnglish
Pages (from-to)757-777
Number of pages21
JournalCommunications in Mathematical Physics
Volume180
Issue number3
DOIs
Publication statusPublished - 1996 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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