Kac-Moody algebras and Lie algebras of regular vector fields on tori

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dc.creatorde Traubenberg, M. Rausch
dc.creatorSlupinski, M. J.
dc.date2001-09-14
dc.date2001-09-20
dc.date.accessioned2026-07-07T11:48:16Z
dc.date.available2026-07-07T11:48:16Z
dc.descriptionWe consider the problem of representing the Kac-Moody algebra $\mathfrak{g}(N)$ specified by an $r\times r$ indecomposable generalised Cartan matrix $N$ as vector fields on the torus ${{\bb C}^*}^r$. It is shown that, if the representations are of a certain form, this is possible if and only if $\mathfrak{g}(N)\cong sl(r+1,{\bb C})$ or $\tilde{sl}(r,{\bb C})$. For $sl(r+1,{\bb C})$ and $\tilde{sl}(r,{\bb C})$, discrete families of representations are constructed. These generalise the well-known discrete families of representations of $sl(2,{\bb C})$ as regular vector fields on ${\bb C}^*$
dc.description20 pages, typo corrected in the title
dc.identifierhttps://arxiv.org/abs/math/0109090
dc.identifierhttp://arxiv.org/abs/math/0109090
dc.identifierJ.Algebra253:189-208,2002
dc.identifierdoi:10.1016/S0021-8693(02)00054-6
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/202860
dc.subjectRepresentation Theory
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subject17B67, 17B10, 16W25
dc.titleKac-Moody algebras and Lie algebras of regular vector fields on tori
dc.typetext

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