Topological invariants of piecewise hereditary algebras

Abstract

We investigate the Galois coverings of piecewise algebras and more particularly their behaviour under derived equivalences. Under a technical assumption which is satisfied if the algebra is derived equivalent to a 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.

The hypotheses of the main theorem were modified: The next now deals mainly with piecewise hereditary algebras which are derived equivalent to a hereditary algebra (instead of all piecewise hereditary algebras in the previous version)

Cited by in corpus (7)

• Crossed-products of Calabi-Yau algebras by finite groups
• The strong global dimension of piecewise hereditary algebras
• $\tau$-Tilting Theory and $\tau$-Slices
• On the first Hochschild cohomology group of a cluster-tilted algebra
• Galois coverings of weakly shod algebras
• Special biserial algebras with no outer derivations
• Piecewise Hereditary algebras of Dynkin and extended Dynkin type