Hamiltonian operators and the classical Yang-Baxter equation

DOI10.1007/BF01077846zbMath0527.58018OpenAlexW2087706116MaRDI QIDQ595246

I. Ya. Dorfman, Israel M. Gel'fand

Publication date: 1983

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01077846

zbMATH Keywords

Lie algebra of vector fieldsHamiltonian manifoldscomplex over a Lie algebrageneralized symplectic structure

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Symplectic manifolds (general theory) (53D05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) de Rham theory in global analysis (58A12) Representations of Lie algebras and Lie superalgebras, analytic theory (17B15) Cohomology of Lie (super)algebras (17B56)

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Cites Work

• Les variétés de Poisson et leurs algèbres de Lie associees
• LOCAL LIE ALGEBRAS
• A simple model of the integrable Hamiltonian equation
• Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian System
• The cohomologies of the lie algebra of the vector fields in a circle
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