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Topological invariants of piecewise hereditary algebras

Patrick Le Meur
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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.

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Patrick Le Meur. 2007-02-15. Topological invariants of piecewise hereditary algebras. https://doi.org/10.1090/s0002-9947-2010-05185-2

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