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Relative Auslander-Reiten sequences for quasi-hereditary algebras

Karin Erdmann; José Antonio de la Peña; Corina Sáenz — 2002

Colloquium Mathematicae

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).

Standardly stratified split and lower triangular algebras

Eduardo do N. Marcos; Hector A. Merklen; Corina Sáenz — 2002

Colloquium Mathematicae

In the first part, we study algebras A such that A = R ⨿ I, where R is a subalgebra and I a two-sided nilpotent ideal. Under certain conditions on I, we show that A is standardly stratified if and only if R is standardly stratified. Next, for $A = [\begin{matrix} U & 0 \\ M & V \end{matrix}]$ , we show that A is standardly stratified if and only if the algebra R = U × V is standardly stratified and $_{V} M$ is a good V-module.

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