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Displaying similar documents to “A splitting theorem for multipeak path algebras”

Iterated coil enlargements of algebras

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)...

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

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 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 - ⊗ 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 ∈ U m o d k G B → m o d ( R / G ) and Ψ U : m o d ( R / G ) → ∏ B ∈ U m o d k G B )is full (resp. strictly full)...

On restrictions of generic modules of tame algebras

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.

Full embeddings of almost split sequences over split-by-nilpotent extensions

Ibrahim Assem, Dan Zacharia (1999)

Colloquium Mathematicae

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Let R be a split extension of an artin algebra A by a nilpotent bimodule A Q A , and let M be an indecomposable non-projective A-module. We show that the almost split sequences ending with M in mod A and mod R coincide if and only if H o m A ( Q , τ A M ) = 0 and M ⊗ A Q = 0 .

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. ...