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Is there any geometric or more direct conceptual way to understand supersymmetry algebra, rather than staring from a lagrangian including boson and fermion fields, deriving all the expressions ensuring the supersymmetric invariance and then writing down the supersymmetry algebra. For geometric/algebraic way I mean to derive the supersymmetry algebra from pure(or partially) geometry(spinors, spin group,.etc). Thanks.

Is there any geometric or more direct conceptual way to understand a supersymmetry algebra, rather than starting from a Lagrangian including boson and fermion fields, deriving all the expressions ensuring the supersymmetry invariance and then writing down the supersymmetry algebra? For a geometric or algebraic way, I mean to (at least partially) derive the supersymmetry algebra from pure geometry  (spinors, spin group, etc.).