arXiv subjects

Yohny Calderón-Henao

Publications and source records attributed to Yohny Calderón-Henao.

2 recordsLinked to original sources

arXiv2023

Relations Between the Strong Global dimension, Complexes of Fixed Size and Derived Category

Let $\mathbb{Z}$ be the integer numbers, $\mathbb{k}$ an algebraically closed field, $Λ$ a finite dimensional $\mathbb{k}$-algebra, mod$Λ$ the category of finitely generated right modules, proj$Λ$ the full subcategory of mod$Λ$ consisting of all projective $Λ$-modules, and $C_n(projΛ)$ the bounded complexes of projective $Λ$-modules of fixed size for any integer $n\geq2$. We found an algorithm to calculate the strong global dimension of $Λ$, when $Λ$ has finite strong global dimension and derived-discrete, using the Auslander-Reiten quivers of the categories $C_n(projΛ)$. Also, we show the relation between the Auslander-Reiten quiver of the bounded derived category $D^b(Λ)$ and the Auslander-Reiten quiver of $C_{η+1}(projΛ)$, where $η=s.gl.dim(Λ)$ (strong global dimension of $Λ$).

math.RT↗

arXiv2019

On irreducible morphisms and Auslander-Reiten triangles in the stable category of modules over repetitive algebras

Let $\mathbf{k}$ be an algebraically closed field, let $Λ$ be a finite dimensional $\mathbf{k}$-algebra, and let $\widehatΛ$ be the repetitive algebra of $Λ$. For the stable category of finitely generated left $\widehatΛ$-modules $\widehatΛ$-\underline{mod}, we show that the irreducible morphisms fall into three canonical forms: (i) all the component morphisms are split monomorphisms; (ii) all of them are split epimorphisms; (iii) there is exactly one irreducible component. We next use this fact in order to describe the shape of the Auslander-Reiten triangles in $\widehatΛ$-\underline{mod}. We use the fact (and prove) that every Auslander-Reiten triangle in $\widehatΛ$-\underline{mod} is induced from an Auslander-Reiten sequence of finitely generated left $\widehatΛ$-modules.

math.RT↗