An extension of the Korteweg-de Vries hierarchy arising from a representation of a toroidal Lie algebra

DOI10.1006/jabr.1998.7788zbMath1016.37039OpenAlexW2018830281WikidataQ115395828 ScholiaQ115395828MaRDI QIDQ1305062

Yuly Billig

Publication date: 20 August 2003

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1998.7788

zbMATH Keywords

toroidal Lie algebrasKdV hierarchysoliton-type solutionsvertex operator representationsextended KdV hierarchy

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Vertex operators; vertex operator algebras and related structures (17B69) Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (9)

Vertex Operator Construction for the Toroidal Lie Algebra of TypeF₄ ⋮ Highest weight modules over pre-exp-polynomial Lie algebras ⋮ On a Certain Fractional q-Difference and its Eigen Function ⋮ Integrable Representations for Twisted Generalized Virasoro-Toroidal Lie Algebras ⋮ Integrable representations for generalized Virasoro-toroidal Lie algebras. ⋮ EULER–POINCARÉ FLOWS ON THE LOOP BOTT–VIRASORO GROUP AND SPACE OF TENSOR DENSITIES AND (2 + 1)-DIMENSIONAL INTEGRABLE SYSTEMS ⋮ On the (2+1)-Dimensional Extension of 1-Dimensional Toda Lattice Hierarchy ⋮ Irreducible representations for toroidal Lie algebras ⋮ On Generalized Intersection Matrix Algebras Arising from 2-Fold Affinization of Cartan Matrices

Cites Work

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• Kähler differentials and coverings of complex simple Lie algebras extended over a commutative algebra
• Toroidal Lie algebras and vertex representations
• Vertex representations for \(n\)-toroidal Lie algebras and a generalization of the Virasoro algebra
• The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group
• Operator Approach to the Kadomtsev-Petviashvili Equation–Transformation Groups for Soliton Equations III–
• Principal vertex operator representations for toroidal Lie algebras

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