Coverings of laura algebras: The standard case

Authors :: Juan Carlos Bustamante
Patrick Le Meur
Ibrahim Assem
Groupe de recherche en théorie des représentations des algèbres
Université de Sherbrooke (UdeS)
Departamento de Matematicas - Universidad San Fransisco de Quito
Universidad San Fransisco de Quito
Centre de Mathématiques et de Leurs Applications (CMLA)
École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS)
Source :: Journal of Algebra, Journal of Algebra, Elsevier, 2010, 323 (1), pp.83--120. ⟨10.1016/j.jalgebra.2009.08.013⟩
Publication Year :: 2010
Publisher :: Elsevier BV, 2010.
Abstract: In this paper, we study the covering theory of laura algebras. We prove that if a connected laura algebra is standard (that is, it is not quasi-tilted of canonical type and its connecting components are standard), then this algebra has nice Galois coverings associated to the coverings of the connecting component. As a consequence, we show that the first Hochschild cohomology group of a standard laura algebra vanishes if and only if it has no proper Galois coverings.<br />The main result on the non-standard case was reformulated due to an inaccuracy in the previous version. Lemma 6.1 was removed due to a simplification. The last section on the special biserial case was removed. Typos corrected and bibliography updated. Final version to appear in Journal of Algebra