Coverings of Laura Algebras: the Standard Case

Ibrahim Assem (1) , Juan Carlos Bustamante (2) , Patrick Le Meur (3)

1 Groupe de recherche en théorie des représentations des algèbres
2 Departamento de Matematicas - Universidad San Fransisco de Quito
3 CMLA - Centre de Mathématiques et de Leurs Applications

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.

Mots clés: Representations of Algebras; Covering Theory; Galois coverings; Laura Algebras; Hochschild Cohomology; Simple Connectedness

Domaines: Théorie des représentations [math.RT]

Ibrahim Assem, Juan Carlos Bustamante, Patrick Le Meur. Coverings of Laura Algebras: the Standard Case. Journal of Algebra, 2010, 323 (1), pp.83--120. ⟨10.1016/j.jalgebra.2009.08.013⟩. ⟨hal-00310452v2⟩