EXTENDED FRACTIONAL SUPERSYMMETRIC QUANTUM-MECHANICS

Recently, we presented a new class of quantum-mechanical Hamiltonians which can be written as the Fth power of a conserved charge: H = Q(F) with F = 2,3,.... This construction, called fractional supersymmetric quantum mechanics, was realized in terms of a paragrassmann variable theta of order F, which satisfies theta(F) = 0. Here, we present an alternative realization of such an algebra in which the internal space of the Hamiltonians is described by a tensor product of two paragrassmann variables of orders F and F-1 respectively. In particular, we find q-deformed relations (where q are roots of unity) between different conserved charges.