A Natural Lie Superalgebra Bundle on Rank Three Wsd Manifolds
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چکیده
We 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 sl(4, C) with the full special linear superalgebras of some graded vector spaces isotypical with respect to a natural action of so(3, R). We provide an explicit description of one of the real forms of this superalgebra, which is geometrically natural being made of so(3, R)-invariant operators which preserve the Poincaré (odd Hermitean) inner product on the bundle of forms.
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تاریخ انتشار 2008