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We determine the structure of the $*$-Lie superalgebra generated by a set ofcarefully chosen natural operators of an orientable WSD manifold of rank three.This Lie superalgebra is formed by global sections of a natural Liesuperalgebra bundle, and turns out to be a product of $\mathbf{sl}(4,\C)$ withthe full special linear superalgebras of some graded vector spaces isotypicalwith respect to a natural action of $\mathbf{so}(3,\R)$. We provide an explicitdescription of one of the real forms of this superalgebra, which isgeometrically natural being made of $\mathbf{so}(3,\R)$-invariant operatorswhich preserve the Poincar\'e (odd Hermitean) inner product on the bundle offorms.

A natural Lie superalgebra bundle on rank three WSD manifolds