2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/179483Fractional supersymmetric quantum mechanics of order $λ$ is realized in terms of the generators of a generalized deformed oscillator algebra and a Z$_λ$-grading structure is imposed on the Fock space of the latter. This realization is shown to be fully reducible with the irreducible components providing $λ$ sets of minimally bosonized operators corresponding to both unbroken and broken cases. It also furnishes some examples of Z$_λ$-graded uniform topological symmetry of type (1, 1, ..., 1) with topological invariants generalizing the Witten index.LaTeX 2e, amssym, 16 pages, no figureMathematical PhysicsHigh Energy Physics - TheoryQuantum AlgebraQuantum Physicstext