Pseudodifferential symbols on Riemann surfaces and Krichever-Novikov algebras

DOI10.1007/s00220-007-0234-2zbMath1140.17019OpenAlexW2121458040MaRDI QIDQ2466815

Dmitry Donin, Boris A. Khesin

Publication date: 16 January 2008

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

Full work available at URL: https://doi.org/10.1007/s00220-007-0234-2

zbMATH Keywords

Riemann surfaceKrichever-Novikov algebraspseudo-differential symbolslogarithmic cocyclemeromorphic pseudo-differential symbol

Mathematics Subject Classification ID

Virasoro and related algebras (17B68) Lie algebras of vector fields and related (super) algebras (17B66) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Lie bialgebras; Lie coalgebras (17B62) Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) (32G34)

Related Items (1)

Formal pseudodifferential operators in one and several variables, central extensions, and integrable systems

Cites Work

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• A central extension of the algebra of pseudodifferential symbols
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• Virasoro-type algebras, Riemann surfaces and strings in Minkowski space
• 2-cocycles on the algebra of differential operators
• Poisson Lie groups, dressing transformations, and Bruhat decompositions
• Some remarks on the cohomology of Krichever-Novikov algebras
• Affine Lie algebras on Riemann surfaces
• Poisson-Lie group of pseudodifferential symbols
• The Lie algebras $ \mathfrak{gl}(\lambda)$ and cohomologies of Lie algebras of differential operators
• Local cocycles and central extensions for multipoint algebras of Krichever-Novikov type
• Dressing transformations and Poisson group actions

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