Simple connectedness of quasitilted algebras

Abstract

Let 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 quiver