  We discuss two independent constructions to introduce an N-extended
Supersymmetric Quantum Mechanics. The first one makes use of the Fierz
identities while the second one (divided into two subcases) makes use of the
Schur lemma. The N supercharges Q_I are square roots of a free Hamiltonian H
given by the tensor product of a D-dimensional Laplacian and a 2d-dimensional
identity matrix operator. We present the mutual relations among N, D and d. The
mod 8 Bott's periodicity of Clifford algebras is encoded, in the Fierz case, in
the Radon-Hurwitz function and, in the Schur case, in an extra independent
function.
