H_T Vertex Algebras and the Infinite Toda Lattice

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dc.creatorBergvelt, Maarten
dc.date2005-05-13
dc.date.accessioned2026-07-07T05:19:53Z
dc.date.available2026-07-07T05:19:53Z
dc.descriptionLet H_T=C[T,T^{-1}] be the Hopf algebra of symmetries of a lattice of rank 1, or equivalently, H_T is the group algebra of a free Abelian group with one generator T. We construct conformal algebras, vertex Poisson algebras and vertex algebras with H_T as symmetry. For example, the Hamiltonian structure for the infinite Toda lattice gives rise to an H_T-vertex Poisson structure on a free difference algebra. Examples of H_T-vertex algebras are constructed from representations of a class of infinite dimensional Lie algebras related to H_T in the same way loop algebras are related to the Hopf algebra H_D=C[D] of infinitesimal translations used in the usual vertex algebras.
dc.description97 pages
dc.identifierhttps://arxiv.org/abs/math/0505289
dc.identifierhttp://arxiv.org/abs/math/0505289
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75190
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subjectMSC-class: 17B69
dc.titleH_T Vertex Algebras and the Infinite Toda Lattice
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