arXiv subjects

Leonardo Salmerón Castro

Publications and source records attributed to Leonardo Salmerón Castro.

3 recordsLinked to original sources

arXiv2026

Generic modules for the category of filtered by standard modules

Here we show that, given a finite homological system $({\cal P},\leq,\{Δ_u\}_{u\in {\cal P}})$ for a finite-dimensional algebra $Λ$ over an algebraically closed field, the category ${\cal F}(Δ)$ of $Δ$-filtered modules is tame if and only if, for any $d\in \mathbb{N}$, there are only finitely many isomorphism classes of generic $Λ$-modules adapted to ${\cal F}(Δ)$ with endolength $d$. We study the relationship between these generic modules and one-parameter families of indecomposables in ${\cal F}(Δ)$. This study applies in particular to the category of modules filtered by standard modules for standardly stratified algebras. This article includes a correction of an error in [8].

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arXiv2024

A representation embedding for algebras of infinite type

We show that for any finite-dimensional algebra $Λ$ of infinite representation type, over a perfect field, there is a bounded principal ideal domain $Γ$ and a representation embedding from $Γ-$mod into $Λ-$mod. As an application, we prove a variation of the Brauer-Trall Conjecture II: finite-dimensional algebras of infinite-representation type admit infinite families of non-isomorphic finite-dimensional indecomposables with fixed endolength, for infinitely many endolengths.

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arXiv2020

Homological systems and bocses

We show that, up to Morita equivalence, any finite-dimensional algebra with a suitable homological system, admits an exact Borel subalgebra. This generalizes a theorem by Koenig, Külshammer and Ovsienko, which holds for quasi-hereditary algebras. Our proof follows the same general scheme proposed by these authors, in a more general context: we associate a differential graded tensor algebra with relations, using the structure of $A_{\infty}-$algebra of a suitable Yoneda algebra, and use its category of modules to describe the category of filtered modules associated to the given homological system.

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