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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Topological invariants of piecewise hereditary algebras


Author: Patrick Le Meur
Journal: Trans. Amer. Math. Soc. 363 (2011), 2143-2170
MSC (2010): Primary 16G10; Secondary 16G60, 16E35, 16E40
Published electronically: November 16, 2010
MathSciNet review: 2746678
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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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Additional Information

Patrick Le Meur
Affiliation: CMLA, ENS Cachan, CNRS, UniverSud, 61 Avenue du President Wilson, F-94230 Cachan, France
Address at time of publication: Laboratoire de Mathématiques, Université Blaise Pascal & CNRS, Complexe Scientifique Les Cézeaux, BP 80026, 63171 Aubière cedex, France
Email: Patrick.LeMeur@cmla.ens-cachan.fr, Patrick.LeMeur@math.univ-bpclermont.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05185-2
PII: S 0002-9947(2010)05185-2
Received by editor(s): March 6, 2009
Received by editor(s) in revised form: July 30, 2009
Published electronically: November 16, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.