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

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 super-algebras of some graded vector spaces isotypical with respect to a natural action of so(3,R). We give an explicit description of a geometrically natural real form of L3,C. This real form is made up of so(3,R)-invariant operators which preserve the Poincaré pairing on the bundle of forms.