Topological invariants of piecewise hereditary algebras
Résumé
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.
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