Orbit algebras that are invariant under stable equivalences of Morita type

Zygmunt Pogorzały

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Trisections of module categories

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Let A be a finite-dimensional algebra over a field k. We discuss the existence of trisections (mod₊ A,mod₀ A,mod₋ A) of the category of finitely generated modules mod A satisfying exactness, standardness, separation and adjustment conditions. Many important classes of algebras admit trisections. We describe a construction of algebras admitting a trisection of their module categories and, in special cases, we describe the structure of the components of the Auslander-Reiten quiver lying...

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Given a convex algebra ∧0 in the tame finite-dimensional basic algebra ∧, over an algebraically closed field, we describe a special type of restriction of the generic ∧-modules.

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Iterated coil enlargements of algebras

Bertha Tomé (1995)

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Let Λ be a finite-dimensional, basic and connected algebra over an algebraically closed field, and mod Λ be the category of finitely generated right Λ-modules. We say that Λ has acceptable projectives if the indecomposable projective Λ-modules lie either in a preprojective component without injective modules or in a standard coil, and the standard coils containing projectives are ordered. We prove that for such an algebra Λ the following conditions are equivalent: (a) Λ is tame, (b)...

Comments on gentleness of endomorphism algebras.

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Properties of G-atoms and full Galois covering reduction to stabilizers

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Given a group G of k-linear automorphisms of a locally bounded k-category R it is proved that the endomorphism algebra $E n d_{R} (B)$ of a G-atom B is a local semiprimary ring (Theorem 2.9); consequently, the injective $E n d_{R} (B)$ -module ${(E n d_{R} (B))}^{*}$ is indecomposable (Corollary 3.1) and the socle of the tensor product functor $- \otimes_{R} B^{*}$ is simple (Theorem 4.4). The problem when the Galois covering reduction to stabilizers with respect to a set U of periodic G-atoms (defined by the functors $Φ^{U} : ∐_{B \in U} m o d k G_{B} \to m o d (R / G)$ and $Ψ^{U} : m o d (R / G) \to \prod_{B \in U} m o d k G_{B}$ )is full (resp. strictly full)...

On Hom-spaces of tame algebras

Raymundo Bautista, Yuriy Drozd, Xiangyong Zeng, Yingbo Zhang (2007)

Open Mathematics

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Let Λ be a finite dimensional algebra over an algebraically closed field k and Λ has tame representation type. In this paper, the structure of Hom-spaces of all pairs of indecomposable Λ-modules having dimension smaller than or equal to a fixed natural number is described, and their dimensions are calculated in terms of a finite number of finitely generated Λ-modules and generic Λ-modules. In particular, such spaces are essentially controlled by those of the corresponding generic modules. ...

Directing components for quasitilted algebras

Flávio Coelho (1999)

Colloquium Mathematicae

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We show here that a directing component of the Auslander-Reiten quiver of a quasitilted algebra is either postprojective or preinjective or a connecting component.