Multiloop realization of extended affine Lie algebras and Lie tori

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dc.creatorAllison, Bruce
dc.creatorBerman, Stephen
dc.creatorFaulkner, John
dc.creatorPianzola, Arturo
dc.date2007-09-07
dc.date2007-09-10
dc.date.accessioned2026-07-07T08:28:08Z
dc.date.available2026-07-07T08:28:08Z
dc.descriptionAn important theorem in the theory of infinite dimensional Lie algebras states that any affine Kac-Moody algebra can be realized (that is to say constructed explicitly) using loop algebras. In this paper, we consider the corresponding problem for a class of Lie algebras called extended affine Lie algebras (EALAs) that generalize affine algebras. EALAs occur in families that are constructed from centreless Lie tori, so the realization problem for EALAs reduces to the realization problem for centreless Lie tori. We show that all but one family of centreless Lie tori can be realized using multiloop algebras (in place of loop algebras). We also obtain necessary and sufficient for two centreless Lie tori realized in this way to be isotopic, a relation that corresponds to isomorphism of the corresponding families of EALAs.
dc.descriptionMarginal notes (for tex labels) deleted
dc.identifierhttps://arxiv.org/abs/0709.0975
dc.identifierhttp://arxiv.org/abs/0709.0975
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137509
dc.subjectRings and Algebras
dc.subjectRepresentation Theory
dc.subject17B65; 17B67; 17B70
dc.titleMultiloop realization of extended affine Lie algebras and Lie tori
dc.typetext

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