Two results on a class of Poisson structures on Lie groups

DOI10.1007/BF02571801zbMath0760.58016WikidataQ115391983 ScholiaQ115391983MaRDI QIDQ1204272

Luen-Chau Li

Publication date: 3 March 1993

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174406

zbMATH Keywords

Hamiltonianmonodromy mapPoisson structures on Lie groups

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (2)

The SVD flows on generic symplectic leaves are completely integrable ⋮ Nonlocal quadratic Poisson algebras, monodromy map, and Bogoyavlensky lattices

Cites Work

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• What is a classical r-matrix?
• Poisson Lie groups, dressing transformations, and Bruhat decompositions
• Completely integrable systems, Euclidean Lie algebras, and curves
• Systems of Toda type, inverse spectral problems, and representation theory
• Poisson geometry of the analog of the Miura maps and Bäcklund-Darboux transformations for equations of Toda type and periodic Toda flows
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• The SVD flows on generic symplectic leaves are completely integrable
• Dressing transformations and Poisson group actions

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