Galois coverings and simple connectedness of piecewise hereditary algebras

Patrick Le Meur (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

Let A a basic connected and finite dimensional piecewise hereditary algebra of type Q. We prove that A admits a universal Galois covering with group the fundamental group of Q. As a corollary, we deduce that A is simply connected if and only if Q is a tree, if and only if the Hocschild cohomology group HH^1(A) vanishes. As an application, we prove that if C->A is a Galois covering with group G, then C is piecewise hereditary of type a Galois covering with group G of Q.

Mots clés: algebra; finite dimensional; piecewise hereditary; cluster; tilting; galois covering; universal cover; simply connected; covering techniques; hochschild cohomology; dg category

Domaines: Théorie des représentations [math.RT]

Patrick Le Meur. Galois coverings and simple connectedness of piecewise hereditary algebras. 2007. ⟨hal-00131235v2⟩