2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128322Let A be a basic connected finite dimensional algebra over an algebraically closed field. Assuming that A is quasitilted, we prove that A is simply connected if and only if its first Hochschild cohomology group HH^1(A) vanishes. This generalises a result of I. Assem, F.U. Coelho and S. Trepode and which proves the same equivalence for tame quasitilted algebras.This note is a complement to the preprint arXiv:math/0702457 of the author and in which the same characterisation of simple connectedness is proved for piecewise hereditary algebras of type a quiverRepresentation Theory16G10; 18G10text