A natural Lie superalgebra bundle on rank three WSD manifolds

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dc.creatorGaiffi, Giovanni
dc.creatorGrassi, Michele
dc.date2007-06-07
dc.date2007-07-12
dc.date.accessioned2026-07-07T08:14:59Z
dc.date.available2026-07-07T08:14:59Z
dc.descriptionWe determine the structure of the $*$-Lie superalgebra generated by a set of carefully chosen natural operators of an orientable WSD manifold of rank three. This Lie superalgebra is formed by global sections of a natural Lie superalgebra bundle, and turns out to be a product of $\mathbf{sl}(4,\C)$ with the full special linear superalgebras of some graded vector spaces isotypical with respect to a natural action of $\mathbf{so}(3,\R)$. We provide an explicit description of one of the real forms of this superalgebra, which is geometrically natural being made of $\mathbf{so}(3,\R)$-invariant operators which preserve the Poincaré (odd Hermitean) inner product on the bundle of forms.
dc.description20 pages, 4 tables. Minor changes in presentation from v1
dc.identifierhttps://arxiv.org/abs/0706.1011
dc.identifierhttp://arxiv.org/abs/0706.1011
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133328
dc.subjectDifferential Geometry
dc.subjectRepresentation Theory
dc.subject53A45; 15A66; 20C15
dc.titleA natural Lie superalgebra bundle on rank three WSD manifolds
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