2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77248We give an elementary argument for the well known fact that the endomorphism algebra $End_Q(A)$ of a simple complex abelian surface $A$ can neither be an imaginary quadratic field nor a definite quaternion algebra. Another consequence of our argument is that a two-dimensional complex torus $T$ with $Q(\sqrt{d})\subseteq End_Q(A)$ where $Q(\sqrt{d})$ is real quadratic, is algebraic.Latex, 4 pagesAlgebraic Geometry14K20, 14K22, 32J20text