2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/38535A generalized anti-hermitian staggered Dirac operator is formulated. Its relation with noncommutative geometry is briefly reviewed. Once this anti-hermitian operator is modified to be ``$γ^5$-hermitian'', it will provide a new solution to Ginsparg-Wilson relation, basing on an abstract algebraic analysis of Neuberger's overlap construction and a redefinition of chirality.REVTEX, 7 pages, no figureHigh Energy Physics - Latticetext