Symplectic geometries on \(T^*\widetilde {G}\), Hamiltonian group actions and integrable systems

DOI10.1016/0393-0440(94)00027-2zbMath0829.53027arXivhep-th/9210095OpenAlexW3101953317MaRDI QIDQ1893847

J. Harnad, Boris A. Kupershmidt

Publication date: 7 August 1995

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9210095

zbMATH Keywords

symplectic structureloop groupsmoment mapsHamiltonian action

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Loops, quasigroups (20N05) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Related Items (11)

Deformed integrableσ-models, classicalR-matrices and classical exchange algebra on Drinfel’d doubles ⋮ Modified systems found by symmetry reduction on the cotangent bundle of a loop group ⋮ Algebraic proofs for shallow water bi-Hamiltonian systems for three cocycle of the semi-direct product of Kac-Moody and Virasoro Lie algebras ⋮ Dirac approach to constrained submanifolds in a double loop group: From Wess-Zumino-Novikov-Witten to Poisson-Lie σ-model ⋮ Algebraic Properties of the Semi-direct Product of Kac–Moody and Virasoro Lie Algebras and Associated Bi-Hamiltonian Systems ⋮ Hamiltonian loop group actions and T-duality for group manifolds ⋮ Integrable systems, multicomponent twisted Heisenberg-Virasoro algebra and its central extensions ⋮ Poisson-Lie \(T\)-duality and non-trivial monodromies ⋮ Integrable geodesic flows and super polytropic gas equations ⋮ Geodesic flows, bi-Hamiltonian structure and coupled KdV type systems ⋮ Hamiltonian Structures on Coadjoint Orbits of Semidirect Product G = Diff+(S 1) ? < C ?(S 1, ?)

Cites Work

• Unnamed Item
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• Non-Abelian bosonization in two dimensions
• Twisted Diff \(S^ 1\)-action on loop groups and representations of the Virasoro algebra
• Super loop groups, Hamiltonian actions and super Virasoro algebras
• Transformation groups of soliton equations. IV: A new hierarchy of soliton equations of KP-type
• Loop groups and equations of KdV type
• Kac-Moody Lie algebras and soliton equations. II: Lax equations associated with \(A_ 1^{(1)}\)
• Reduction of Hamiltonian systems, affine Lie algebra, and Lax equations. II
• Mathematics of dispersive water waves
• Isospectral Hamiltonian flows in finite and infinite dimensions. II: Integration of flows
• Constrained Hamiltonian systems on Lie groups, moment map reductions, and central extensions
• The spectral theory of a functional-difference operator in conformal field theory
• MODIFIED KORTEWEG-DE VRIES EQUATIONS ON EUCLIDEAN LIE ALGEBRAS
• On the quasi-Hamiltonian formalism of the KdV equation

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