Expanding Lie (super)algebras through abelian semigroups

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dc.creatorIzaurieta, Fernando
dc.creatorRodríguez, Eduardo
dc.creatorSalgado, Patricio
dc.date2006-06-21
dc.date2006-11-30
dc.date.accessioned2026-07-07T11:06:44Z
dc.date.available2026-07-07T11:06:44Z
dc.descriptionWe propose an outgrowth of the expansion method introduced by de Azcarraga et al. [Nucl. Phys. B 662 (2003) 185]. The basic idea consists in considering the direct product between an abelian semigroup S and a Lie algebra g. General conditions under which relevant subalgebras can systematically be extracted from S \times g are given. We show how, for a particular choice of semigroup S, the known cases of expanded algebras can be reobtained, while new ones arise from different choices. Concrete examples, including the M algebra and a D'Auria-Fre-like Superalgebra, are considered. Finally, we find explicit, non-trace invariant tensors for these S-expanded algebras, which are essential ingredients in, e.g., the formulation of Supergravity theories in arbitrary space-time dimensions.
dc.description42 pages, 8 figures. v2: Improved figures, updated notation and terminology
dc.identifierhttps://arxiv.org/abs/hep-th/0606215
dc.identifierhttp://arxiv.org/abs/hep-th/0606215
dc.identifierJ.Math.Phys.47:123512,2006
dc.identifierdoi:10.1063/1.2390659
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/189615
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleExpanding Lie (super)algebras through abelian semigroups
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