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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., 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

Let Γ be a connected component of the Auslander–Reiten quiver Γ (mod A ) of an Artin algebra. We show that Γ is quasi-directed if and only if the paths in ind A , having end-points in Γ , satisfy certain conditions. Moreover, we describe the shapes of such components and identify the classes of algebras to which they are related.

In this paper, we define and study a special type of trisections in a module category, namely the compact trisections which characterize quasi-directed components. We apply this notion to the study of laura algebras and we use it to define a class of algebras with predictable Auslander–Reiten components.

We prove that if A is an artin algebra, G is a finite group acting on A such that |G| is invertible in A, and R=A[G]b is a basic algebra associated with the skew group algebra, then A is left supported (or right supported, or laura, or left glued, or right glued, or weakly shod, or shod) if and only if so is R. Fil: Assem, Ibrahim. University of Sherbrooke; Canadá Fil: Lanzilotta, Marcelo. Universidad de la República; Uruguay Fil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina

In this paper, we study, for an artin algebra, the class L A (and R A ) which is a full subcategory of the category modA of finitely generated A-modules, and which consists of all indecomposable A-modules whose predecessors (and successors) have projective dimension (and injective dimension, respectively) at most one. We consider quotient algebras of A, which contain the information on these classes, then define and characterize those algebras for which the class is L A is contravariantly finite (and R A is covariantly finite, respectively).

In this paper, we propose a generalization for the class of laura algebras, which we call almost laura. We show that this new class of algebras retains most of the essential features of laura algebras, especially concerning the important role played by the non-semiregular components in their Auslander-Reiten quivers. Also, we study more intensively the left supported almost laura algebras, showing that these are characterized by the presence of a generalized standard, convex and faithful component. Finally, we prove that almost laura algebras behave well with respect to full subcategories, split-by-nilpotent extensions and skew group algebras., 21 pages, very minor changes, to appear in J. Algebra

We prove that the representation dimension of a tilted, or of a strict laura algebra, is at most three. Fil: Assem, Ibrahim. University of Sherbrooke; Canadá Fil: Platzeck, Maria Ines. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina Fil: Trepode, Sonia Elisabet. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina