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On restrictions of generic modules of tame algebras

Raymundo Bautista, Efrén Pérez, Leonardo Salmerón (2013)

Open Mathematics

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.

On self-injective algebras of finite representation type

Marta Błaszkiewicz, Andrzej Skowroński (2012)

Colloquium Mathematicae

We describe the structure of finite-dimensional self-injective algebras of finite representation type over a field whose stable Auslander-Reiten quiver has a sectional module not lying on a short chain.

On selfinjective algebras of tilted type

Andrzej Skowroński, Kunio Yamagata (2015)

Colloquium Mathematicae

We provide a characterization of all finite-dimensional selfinjective algebras over a field K which are socle equivalent to a prominent class of selfinjective algebras of tilted type.

On split-by-nilpotent extensions

Ibrahim Assem, Dan Zacharia (2003)

Colloquium Mathematicae

Let A and R be two artin algebras such that R is a split extension of A by a nilpotent ideal. We prove that if R is quasi-tilted, or tame and tilted, then so is A. Moreover, generalizations of these properties, such as laura and shod, are also inherited. We also study the relationship between the tilting R-modules and the tilting A-modules.

On the category of modules of second kind for Galois coverings

Piotr Dowbor (1996)

Fundamenta Mathematicae

Let F: R → R/G be a Galois covering and m o d 1 ( R / G ) (resp. m o d 2 ( R / G ) ) be a full subcategory of the module category mod (R/G), consisting of all R/G-modules of first (resp. second) kind with respect to F. The structure of the categories ( m o d ( R / G ) ) / [ m o d 1 ( R / G ) ] and m o d 2 ( R / G ) is given in terms of representation categories of stabilizers of weakly-G-periodic modules for some class of coverings.

On wings of the Auslander-Reiten quivers of selfinjective algebras

Marta Kwiecień, Andrzej Skowroński (2005)

Colloquium Mathematicae

We give necessary and sufficient conditions for a wing of an Auslander-Reiten quiver of a selfinjective algebra to be the wing of the radical of an indecomposable projective module. Moreover, a characterization of indecomposable Nakayama algebras of Loewy length ≥ 3 is obtained.

Orbit algebras that are invariant under stable equivalences of Morita type

Zygmunt Pogorzały (2014)

Open Mathematics

In this note we show that there are a lot of orbit algebras that are invariant under stable equivalences of Morita type between self-injective algebras. There are also indicated some links between Auslander-Reiten periodicity of bimodules and noetherianity of their orbit algebras.

Piecewise hereditary algebras under field extensions

Jie Li (2021)

Czechoslovak Mathematical Journal

Let A be a finite-dimensional k -algebra and K / k be a finite separable field extension. We prove that A is derived equivalent to a hereditary algebra if and only if so is A k K .

Real representations of quivers

Lidia Hügeli, Sverre Smalø (1999)

Colloquium Mathematicae

The Dynkin and the extended Dynkin graphs are characterized by representations over the real numbers.

Currently displaying 61 – 80 of 110