Bihamiltonian reductions and \({\mathcal W}_n\)-algebras

DOI10.1016/S0393-0440(97)00060-0zbMath0953.37014arXivsolv-int/9707017OpenAlexW2031495541MaRDI QIDQ1299240

Gregorio Falqui, Marco Pedroni, Paolo Casati, Franco Magri

Publication date: 15 September 2000

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

Full work available at URL: https://arxiv.org/abs/solv-int/9707017

zbMATH Keywords

Poisson bracketsMarsden-Ratiu reductionloop algebras\({\mathcal W}_n\)-algebraAdler-Gel'fand-Dickey bracketsbi-Hamiltonian reductionGel'fand-Dickey theory

Mathematics Subject Classification ID

Groups and algebras in quantum theory and relations with integrable systems (81R12) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (max. 100)

Poisson pencils: reduction, exactness, and invariants ⋮ On classification and construction of algebraic Frobenius manifolds ⋮ A super hierarchy of the vector nonlinear Schrödinger equations and Hamiltonian structures, conservation laws ⋮ \(W\)-algebras and the equivalence of bihamiltonian, Drinfeld-Sokolov and Dirac reductions ⋮ The soliton equations associated with the affine Kac-Moody Lie algebra \(G_{2}^{(1)}\) ⋮ A super hierarchy of coupled derivative nonlinear Schrödinger equations and conservation laws ⋮ Boussinesq hierarchy and bi-Hamiltonian geometry

Cites Work

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• Quantization of the Drinfel'd-Sokolov reduction.
• Higher spin fields and the Gelfand-Dickey algebra
• Quantization of the Gel'fand-Dikiĭ brackets
• Lie algebras and equations of Korteweg-de Vries type
• Reduction of Poisson manifolds
• The Gel'fand-Dikij Lie algebras and the Virasoro algebra
• Algebraic aspects of nonlinear differential equations
• Classical \(W\)-algebras
• Drinfeld-Sokolov reduction on a simple Lie algebra from the bihamiltonian point of view
• Fractional powers of operators and Hamiltonian systems
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• \(W\)-algebras and superalgebras from constrained WZW models: A group theoretical classification
• Lectures on classical \(W\)-algebras
• Generalized Drinfel'd-Sokolov hierarchies. II: The Hamiltonian structures
• Lie algebras of differential operators, their central extensions, and W- algebras
• Equivalence of the Drinfeld-Sokolov reduction to a bi-Hamiltonian reduction
• The algebra of differential operators on the circle and \(W^{(q)}_{\text{KP}}\)
• Conformal field theories via Hamiltonian reduction
• KP Hierarchies of Orthogonal and Symplectic Type–Transformation Groups for Soliton Equations VI–
• AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS
• A note on fractional KdV hierarchies
• ON THE BIHAMILTONIAN INTERPRETATION OF THE LAX FORMALISM

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