2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115608Let A be a hereditary algebra over an algebraically closed field. We prove that an exact fundamental domain for the m-cluster category of A is the m-left part of the m-replicated algebra $A^{(m)}$ of A. Moreover, we obtain a one-to-one correspondence between the tilting objects in the m-cluster category (that is, the m-clusters) and those tilting $A^{(m)}$-modules for which all non projective-injective direct summands lie in the m-left part of $A^{(m)}$.28 pages, 2 figuresRepresentation TheoryRings and Algebras16G20, 16G70, 16E10 (Primary) 18E30 (Secondary)text