Symmetries of hyper-Kähler (or Poisson gauge field) hierarchy

DOI10.1063/1.528686zbMath0718.53050OpenAlexW1970044936MaRDI QIDQ5749924

Kanehisa Takasaki

Publication date: 1990

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.528686

zbMATH Keywords

hyper-Kähler metricsPoisson algebrainfinitesimal transformationsmembrane theoryPlebanski key functionsfinite symmetries

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Quantum field theory; related classical field theories (81T99)

Related Items (14)

CLOSED N=2 STRINGS: PICTURE-CHANGING, HIDDEN SYMMETRIES AND SDG HIERARCHY ⋮ Dressing operator approach to Moyal algebraic deformation of selfdual gravity ⋮ Nonabelian KP hierarchy with Moyal algebraic coefficients ⋮ Three dimensional reductions of four-dimensional quasilinear systems ⋮ On the dispersionless Davey–Stewartson hierarchy: Zakharov–Shabat equations, twistor structure, and Lax–Sato formalism ⋮ On the associativity of 1-loop corrections to the celestial operator product in gravity ⋮ Chiral higher spin theories and self-duality ⋮ Symmetries and tau function of higher dimensional dispersionless integrable hierarchies ⋮ SDiff(2) Toda equation --- hierarchy, tau function, and symmetries ⋮ On the integrability of symplectic Monge-Ampère equations ⋮ A class of multidimensional integrable hierarchies and their reductions ⋮ Quantum and classical aspects of deformed \(c=1\) strings ⋮ Dispersionless hierarchies, Hamilton-Jacobi theory and twistor correspondences ⋮ Quasiclassical limit of KP hierarchy, \(W\)-symmetries, and free fermions

Cites Work

• Hierarchy structure in integrable systems of gauge fields and underlying Lie algebras
• A new approach to the self-dual Yang-Mills equations
• A connection between the Einstein and Yang-Mills equations
• Nonlinear gravitons and curved twistor theory
• Aspects of integrability in self-dual Einstein metrics and related equations
• An infinite hierarchy of conservation laws and nonlinear superposition principles for self-dual Einstein spaces
• Symmetries of the self-dual Einstein equations. I. The infinite-dimensional symmetry group and its low-dimensional subgroups
• An infinite number of hidden variables in hyper-Kähler metrics
• On the quantum mechanics of supermembranes

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