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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2011

Topological invariants of piecewise hereditary algebras

Résumé

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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Dates et versions

hal-00131235 , version 1 (15-02-2007)
hal-00131235 , version 2 (02-05-2007)
hal-00131235 , version 3 (08-08-2008)
hal-00131235 , version 4 (26-02-2009)

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Patrick Le Meur. Topological invariants of piecewise hereditary algebras. Transactions of the American Mathematical Society, 2011, 363 (4), pp.2143--2170. ⟨10.1090/S0002-9947-2010-05185-2⟩. ⟨hal-00131235v4⟩
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