Geometric interpretation of Supersymmetry

Question

Is there a geometric interpretation of supersymmetry? I.e., if one has a manifold $\mathcal {M} $, and there are $\mathcal {N} $ SUSY generators, then is there a geometric interpretation of the SUSY generators?

Answer 1

Since they are tied to groups, and groups are tied to with geometry, one would expect so. From the wiki article on supersymmetry:

Supersymmetry can be reinterpreted in the language of noncommutative geometry and quantum groups. In particular, it involves a mild form of noncommutativity, namely supercommutativity. See the main article for more details.