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Iterated coil enlargements of algebras

Bertha Tomé (1995)

Fundamenta Mathematicae

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) the Tits form...

Iterated tilted and tilted stably hereditary algebras

Jessica Lévesque (2003)

Colloquium Mathematicae

We prove that a stably hereditary bound quiver algebra A = KQ/I is iterated tilted if and only if (Q,I) satisfies the clock condition, and that in this case it is of type~Q. Furthermore, A is tilted if and only if (Q,I) does not contain any double-zero.

Jordan types for indecomposable modules of finite group schemes

Rolf Farnsteiner (2014)

Journal of the European Mathematical Society

In this article we study the interplay between algebro-geometric notions related to π -points and structural features of the stable Auslander-Reiten quiver of a finite group scheme. We show that π -points give rise to a number of new invariants of the AR-quiver on one hand, and exploit combinatorial properties of AR-components to obtain information on π -points on the other. Special attention is given to components containing Carlson modules, constantly supported modules, and endo-trivial modules.

Laura algebras and quasi-directed components

Marcelo Lanzilotta, David Smith (2006)

Colloquium Mathematicae

Using a notion of distance between indecomposable modules we deduce new characterizations of laura algebras and quasi-directed Auslander-Reiten components. Afterwards, we investigate the infinite radical of Artin algebras and show that there exist infinitely many non-directing modules between two indecomposable modules X and Y if r a d A ∞ ( X , Y ) ≠ 0 . We draw as inference that a convex component is quasi-directed if and only if it is almost directed.

Left sections and the left part of an artin algebra

Ibrahim Assem (2009)

Colloquium Mathematicae

We define a notion of left section in an Auslander-Reiten component, by weakening one of the axioms for sections. We derive a generalisation of the Liu-Skowroński criterion for tilted algebras, then apply our results to describe the Auslander-Reiten components lying in the left part of an artin algebra.

Left-right projective bimodules and stable equivalences of Morita type

Zygmunt Pogorzały (2001)

Colloquium Mathematicae

We study a connection between left-right projective bimodules and stable equivalences of Morita type for finite-dimensional associative algebras over a field. Some properties of the category of all finite-dimensional left-right projective bimodules for self-injective algebras are also given.

Left-sided quasi-invertible bimodules over Nakayama algebras

Zygmunt Pogorzały (2005)

Open Mathematics

Bimodules over triangular Nakayama algebras that give stable equivalences of Morita type are studied here. As a consequence one obtains that every stable equivalence of Morita type between triangular Nakayama algebras is a Morita equivalence.

Lie derivations of dual extensions of algebras

Yanbo Li, Feng Wei (2015)

Colloquium Mathematicae

Let K be a field and Γ a finite quiver without oriented cycles. Let Λ := K(Γ,ρ) be the quotient algebra of the path algebra KΓ by the ideal generated by ρ, and let 𝒟(Λ) be the dual extension of Λ. We prove that each Lie derivation of 𝒟(Λ) is of the standard form.

Limits of tilting modules

Clezio A. Braga, Flávio U. Coelho (2009)

Colloquium Mathematicae

We study the problem of when a direct limit of tilting modules is still a tilting module.

Locally adequate semigroup algebras

Yingdan Ji, Yanfeng Luo (2016)

Open Mathematics

We build up a multiplicative basis for a locally adequate concordant semigroup algebra by constructing Rukolaĭne idempotents. This allows us to decompose the locally adequate concordant semigroup algebra into a direct product of primitive abundant [...] 0-J* 0 - 𝒥 * -simple semigroup algebras. We also deduce a direct sum decomposition of this semigroup algebra in terms of the [...] ℛ* ℛ * -classes of the semigroup obtained from the above multiplicative basis. Finally, for some special cases, we provide a description...

Currently displaying 241 – 260 of 630