Knizhnik-Zamolodchikov equations for positive genus and Krichever-Novikov algebras

DOI10.1070/RM2004v059n04ABEH000760zbMath1066.17014OpenAlexW1968963303MaRDI QIDQ4654288

Martin Schlichenmaier, Oleg K. Sheinman

Publication date: 3 March 2005

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rm2004v059n04abeh000760

zbMATH Keywords

conformal field theoryKrichever-Novikov algebrasKnizhnik-Zamolodchikov equations

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Virasoro and related algebras (17B68) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Infinite-dimensional Lie (super)algebras (17B65) Homological methods in Lie (super)algebras (17B55) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Graded Lie (super)algebras (17B70) Global Riemannian geometry, including pinching (53C20) Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras (17-02) Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) (32G34)

Related Items (10)

N-point Virasoro algebras are multipoint Krichever–Novikov-type algebras ⋮ Simple superelliptic Lie algebras ⋮ Global geometric deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebras ⋮ Quantization of integrable systems with spectral parameter on a Riemann surface ⋮ Deformations of Lie algebras of vector fields arising from families of schemes ⋮ Global geometric deformations of current algebras as Krichever-Novikov type algebras ⋮ Krichever-Novikov algebras, their representations and applications in geometry and mathematical physics ⋮ Representations for three-point Lie algebras of genus zero ⋮ Quantization of Lax integrable systems and conformal field theory ⋮ From the Virasoro Algebra to Krichever–Novikov Type Algebras and Beyond

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