On locally bounded categories stably equivalent to the repetitive algebras of tubular algebras
Zygmunt Pogorzały (1997)
Colloquium Mathematicae
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Zygmunt Pogorzały (1997)
Colloquium Mathematicae
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José A. de la Peña, Idun Reiten (2007)
Colloquium Mathematicae
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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...
Raymundo Bautista, Efrén Pérez, Leonardo Salmerón (2013)
Open Mathematics
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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.
Daniel Simson (1991)
Fundamenta Mathematicae
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Helmut Lenzing, Andrzej Skowroński (1996)
Colloquium Mathematicae
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A.Ya. Helemskii (1994)
Extracta Mathematicae
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Bertha Tomé (1995)
Fundamenta Mathematicae
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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)...
Zimmermann, Alexander (2003)
AMA. Algebra Montpellier Announcements [electronic only]
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Piotr Dowbor (2000)
Colloquium Mathematicae
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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 of a G-atom B is a local semiprimary ring (Theorem 2.9); consequently, the injective -module is indecomposable (Corollary 3.1) and the socle of the tensor product functor 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 and )is full (resp. strictly full)...
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. ...
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.