Generalization of Supersymmetric Quantum Mechanics

A generalization of supersymmetric quantummechanics can be obtained in two different ways usingthe theory of the q-deformation of the oscillatoralgebra, according to whether q is a root of unity ornot. In the first case the fractional supersymmetricquantum mechanic is between bosons and q-bosons. In thesecond case we obtain the deformed supersymmetricquantum mechanics by considering bosons and a deformed truncated oscillator algebra.