2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75383The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra A of finite type can be realized as a Hall algebra, called the exceptional Hall algebra, of the cluster category. This realization provides a natural basis for A. We prove new results and formulate conjectures on `good basis' properties, positivity, denominator theorems and toric degenerations.31 pages, typos correctedRepresentation TheoryRings and Algebras16G20; 18E30text