Current algebras on Riemann surfaces. New results and applications.

DOI10.1515/9783110264524zbMath1258.81002OpenAlexW4234241079MaRDI QIDQ437803

Oleg K. Sheinman

Publication date: 19 July 2012

Published in: De Gruyter Expositions in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/9783110264524

zbMATH Keywords

conformal field theoryKrichever-Novikov algebrasLax integrable systems

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Lie algebras of vector fields and related (super) algebras (17B66) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70) Research exposition (monographs, survey articles) pertaining to quantum theory (81-02) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Groups and algebras in quantum theory and relations with integrable systems (81R12) Applications of Lie algebras and superalgebras to integrable systems (17B80) Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants) (14J80) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21)

Related Items (18)

Lax operator algebras and gradings on semi-simple Lie algebras ⋮ Hierarchies of finite-dimensional Lax equations with a spectral parameter on a Riemann surface and semisimple Lie algebras ⋮ Krichever–Novikov Type Algebras. A General Review and the Genus Zero Case ⋮ Module structure of the center of the universal central extension of a genus zero Krichever-Novikov algebra ⋮ Matrix divisors on Riemann surfaces and Lax operator algebras ⋮ Spectral curves of the hyperelliptic Hitchin systems ⋮ Semisimple Lie algebras and Hamiltonian theory of finite-dimensional Lax equations with spectral parameter on a Riemann surface ⋮ Almost graded current algebras on the symmetric square of a curve ⋮ N-point Virasoro algebras are multipoint Krichever–Novikov-type algebras ⋮ Unnamed Item ⋮ Lax operator algebras of type \(G_{2}\) ⋮ Hitchin systems on hyperelliptic curves ⋮ Quantization of integrable systems with spectral parameter on a Riemann surface ⋮ Certain reductions of Hitchin systems of rank 2 and genera 2 and 3 ⋮ On the universal central extension of hyperelliptic current algebras ⋮ Quantization of Lax integrable systems and conformal field theory ⋮ Families of orthogonal Laurent polynomials, hyperelliptic lie algebras and elliptic integrals ⋮ From the Virasoro Algebra to Krichever–Novikov Type Algebras and Beyond

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