Topological invariants of piecewise hereditary algebras

Patrick Le Meur (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

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.

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

Domaines: Théorie des représentations [math.RT]

Patrick Le Meur. Topological invariants of piecewise hereditary algebras. 2008. ⟨hal-00131235v3⟩