Irreducible representations of supersymmetric quantum mechanics

We present an algorithmic classification of the linear irreducible representations of the N -extended one-dimensional supersymmetry algebra. The analysis is based on the properties of the Clifford algebras associated to the representations of N -extended supersymmetry. The classification is given in three levels: (I) up to the number of bosonic (or ferrnionic) fields entering an irreducible multiplet, (2) up to the number of fields with different mass dimensions (fields content) for each N, and (3) up to the connectivities of the associated graphs for a given field content.