Displaying similar documents to “Radicals of symmetric cellular algebras”

Strong no-loop conjecture for algebras with two simples and radical cube zero

Bernt T. Jensen (2005)

Colloquium Mathematicae

Similarity:

Let Λ be an artinian ring and let 𝔯 denote its Jacobson radical. We show that a simple module of finite projective dimension has no self-extensions when Λ is graded by its radical, with at most two simple modules and 𝔯⁴ = 0, in particular, when Λ is a finite-dimensional algebra over an algebraically closed field with at most two simple modules and 𝔯³ = 0.

Tilting slice modules over minimal 2-fundamental algebras

Zygmunt Pogorzały, Karolina Szmyt (2008)

Colloquium Mathematicae

Similarity:

A class of finite-dimensional algebras whose Auslander-Reiten quivers have starting but not generalized standard components is investigated. For these components the slices whose slice modules are tilting are considered. Moreover, the endomorphism algebras of tilting slice modules are characterized.

Limits of tilting modules

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

Colloquium Mathematicae

Similarity:

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

Relative Auslander-Reiten sequences for quasi-hereditary algebras

Karin Erdmann, José Antonio de la Peña, Corina Sáenz (2002)

Colloquium Mathematicae

Similarity:

Let A be a finite-dimensional algebra which is quasi-hereditary with respect to the poset (Λ, ≤), with standard modules Δ(λ) for λ ∈ Λ. Let ℱ(Δ) be the category of A-modules which have filtrations where the quotients are standard modules. We determine some inductive results on the relative Auslander-Reiten quiver of ℱ(Δ).

On split-by-nilpotent extensions

Ibrahim Assem, Dan Zacharia (2003)

Colloquium Mathematicae

Similarity:

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.