arXiv subjects

Ivon Dorado

Publications and source records attributed to Ivon Dorado.

5 recordsLinked to original sources

arXiv2026

Functorial embeddings associated with the Four Subspace Problem

We define a unified categorical framework for studying six subproblems arising from the classical Four Subspace Problem. For each subproblem, we construct a functor from its associated category to the category of representations of the quiver corresponding to the Four Subspace Problem. This approach gives a common structural setting for the six cases considered and allows a simultaneous and coherent analysis via functorial methods. We prove that the six functors are additive and fully faithful, and we show that none of them is dense. As a consequence, each functor induces an equivalence between the corresponding source category and a well-identified full subcategory of the target category. These equivalences provide an effective mechanism for transferring classification results and structural properties, thereby clarifying the structural interrelations among the categories studied.

math.RT↗

arXiv2025

On a classification problem for a quiver of type $\widetilde{A}_{3}$

We present a new solution to the classification problem for the category of representations of a quiver of type $\widetilde{A}_{3}$. Our approach uses linear algebra techniques which lead us to a reduction that allows to use induction. As an application, the solution to the classical Kronecker problem and its contragredient version are obtained in an elementary way. We also describe the endomorphism rings for the indecomposable representations and an algorithm that shows how to reconstruct their matrix form from some graphic invariants.

math.RT↗

arXiv2019

Deducing factoring methods through concrete material

We formulate and prove a criterion for reducibility of a quadratic polynomial over the integers. The main theorem was suggested by the teaching experience with the concrete material called "the polynomial box". Through the corollaries we relate our theorem and the use of concrete material with some well know factoring methods for quadratic polynomial with integer coeficients.

math.HO↗

arXiv2018

Representations and corepresentations of $p$-equipped posets

For $p$ a prime number and $\mathscr{P}$ a $p$-equipped finite partially ordered set we construct two different right-peak algebras (in the sense of \cite{KS}) $Λ^{(r)}$ and $Λ^{(c)}$. We consider the category $\mathcal{U}^{(r)}$ $\left(\mathcal{U}^{(c)}\right)$ consisting of the finitely generated right $Λ^{(r)}$-modules ($Λ^{(c)}$-modules) which are socle-projective. The categories $\mathcal{U}^{(r)}$ and $\mathcal{U}^{(c)}$ have almost split sequences. We describe he Auslander-Reiten components $\mathcal{C}_{\mathcal{U}}^{(r)}$ and $\mathcal{C}_{\mathcal{U}}^{(c)}$ of the corresponding simple projective modules in $\mathcal{U}^{(r)}$ and $\mathcal{U}^{(c)}$. Then we prove that there is a bijective correspondence between $\mathcal{C}_{\mathcal{U}}^{(r)}$ and $\mathcal{C}_{\mathcal{U}}^{(c)}$, although the corresponding almost split sequences have different shapes.

math.RT↗

arXiv2015

Algebraically equipped posets

We introduce partially ordered sets (posets) with an additional structure given by a collection of vector subspaces of an algebra $A$. We call them algebraically equipped posets. Some particular cases of these, are generalized equipped posets and $p$-equipped posets, for a prime number $p$. We study their categories of representations and establish equivalences with some module categories, categories of morphisms and a subcategory of representations of a differential tensor algebra. Through this, we obtain matrix representations and its corresponding matrix classification problem.

math.RT↗