2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111430We study Laurent expansions of cluster variables in a cluster algebra of rank 2 associated to a generalized Kronecker quiver. In the case of the ordinary Kronecker quiver, we obtain explicit expressions for Laurent expansions of the elements of the canonical basis for the corresponding cluster algebra.19 pages; v2: added Remark 5.7; v3: minor editorial changes, final version to appear in Moscow Math. Journal; v4: more minor editorial changesRepresentation TheoryAlgebraic GeometryCombinatoricstext