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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Topological invariants of piecewise hereditary algebras
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by Patrick Le Meur PDF
Trans. Amer. Math. Soc. 363 (2011), 2143-2170 Request permission

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
  • Received by editor(s): March 6, 2009
  • Received by editor(s) in revised form: July 30, 2009
  • Published electronically: November 16, 2010
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 2143-2170
  • MSC (2010): Primary 16G10; Secondary 16G60, 16E35, 16E40
  • DOI: https://doi.org/10.1090/S0002-9947-2010-05185-2
  • MathSciNet review: 2746678