Global Geometric Deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebra

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dc.creatorFialowski, Alice
dc.creatorSchlichenmaier, Martin
dc.date2006-10-27
dc.date.accessioned2026-07-07T11:28:14Z
dc.date.available2026-07-07T11:28:14Z
dc.descriptionIn two earlier articles we constructed algebraic-geometric families of genus one (i.e. elliptic) Lie algebras of Krichever-Novikov type. The considered algebras are vector fields, current and affine Lie algebras. These families deform the Witt algebra, the Virasoro algebra, the classical current, and the affine Kac-Moody Lie algebras respectively. The constructed families are not equivalent (not even locally) to the trivial families, despite the fact that the classical algebras are formally rigid. This effect is due to the fact that the algebras are infinite dimensional. In this article the results are reviewed and developed further. The constructions are induced by the geometric process of degenerating the elliptic curves to singular cubics. The algebras are of relevance in the global operator approach to the Wess-Zumino-Witten-Novikov models appearing in the quantization of Conformal Field Theory.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0610851
dc.identifierhttp://arxiv.org/abs/math/0610851
dc.identifierInt.J.Theor.Phys.46:2708-2724,2007
dc.identifierdoi:10.1007/s10773-007-9383-5
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/196376
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subject17B66, 17B56, 17B65, 17B68, 14D15, 14H52, 30F30, 81T40
dc.titleGlobal Geometric Deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebra
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