2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120700In this talk we review the classification of the irreducible representations of the algebra of the N-extended one-dimensional supersymmetric quantum mechanics presented in hep-th/0511274. We answer some issues raised in hep-th/0611060, proving the agreement of the results here contained with those in hep-th/0511274. We further show that the fusion algebra of the 1D N-extended supersymmetric vacua introduced in hep-th/0511274 admits a graphical presentation. The N=2 graphs are here explicitly presented for the first time.9 pages, 4 figures, talk given at the 22nd Max Born Symposium in honour of the 70th birthday of Prof. J. Lukierski, Wroclaw, Sept. 2006High Energy Physics - Theorytext