Abstract :

We investigate the Galois coverings of piecewise hereditary algebras. In particular, we study their behaviour under derived equivalences. For a piecewise hereditary algebra, we prove that there exists a universal Galois covering whose group of automorphisms is free and depends only on the derived category of the algebra. As a corollary, we prove that the algebra is simply connected if and only if its first Hochschild cohomology vanishes.