We prove the existence of a natural ∗-Lie super-algebra bundle on any orientable WSD manifold of rank 3. We describe in detail the associated Lie super-algebra L3,C of global sections. We show that L3,C is 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). Wegive an explicit description of a geometrically natural real form ofL3,C. This real form is made up of so(3, R)-invariant operators which preserve the Poincaré pairing on the bundle of forms.

A natural Lie super-algebra bundle on rank 3 WSD manifolds

GAIFFI, GIOVANNI;GRASSI, MICHELE
2009

Abstract

We prove the existence of a natural ∗-Lie super-algebra bundle on any orientable WSD manifold of rank 3. We describe in detail the associated Lie super-algebra L3,C of global sections. We show that L3,C is 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). Wegive an explicit description of a geometrically natural real form ofL3,C. This real form is made up of so(3, R)-invariant operators which preserve the Poincaré pairing on the bundle of forms.
Gaiffi, Giovanni; Grassi, Michele
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/203584
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