arXiv subjects

Jhony F. Caranguay-Mainguez

Publications and source records attributed to Jhony F. Caranguay-Mainguez.

4 recordsLinked to original sources

arXiv2025

About UMP algebras and a special classification case

The class of UMP algebras arises in several classification problems in the context of derived categories of finite-dimensional algebras. In this paper we define the class of UMP algebras and develop algebraic combinatorics tools in order to present a characterization of this class of algebras which are locally monomial (see Definition 4.1) and special multiserial algebras. Among other things, we describe the ramifications graph of symmetric special biserial algebras and we classify which of them are UMP algebras in terms of their bound quivers and their associated Brauer graphs.

math.RT↗

arXiv2025

On universal deformation rings and stable homogeneous tubes

Let $\mathbf{k}$ be a field of any characteristic and let $Λ$ be a finite dimensional $\mathbf{k}$-algebra. We prove that if $V$ is a finite dimensional right $Λ$-module that lies in the mouth of a stable homogeneous tube $\mathfrak{T}$ of the Auslander-Reiten quiver $Λ$ with $\underline{\mathrm{End}}_Λ(V)$ a division ring, then $V$ has a versal deformation ring $R(Λ,V)$ isomorphic to $\mathbf{k}[\![t]\!]$. As consequence we obtain that if $\mathbf{k}$ is algebraically closed, $Λ$ is a symmetric special biserial $\mathbf{k}$-algebra and $V$ is a band $Λ$-module with $\underline{\mathrm{End}}_Λ(V) \cong \mathbf{k}$ that lies in the mouth of its homogeneous tube, then $R(Λ,V)$ is universal and isomorphic to $\mathbf{k}[\![t]\!]$.

math.RT↗

arXiv2025

Universal deformation rings of a special class of modules over generalized Brauer tree algebras

Let $\Bbbk$ be an algebraically closed field and $Λ$ a generalized Brauer tree algebra over $\Bbbk$. We compute the universal deformation rings of the periodic string modules over $Λ$. Moreover, for a specific class of generalized Brauer tree algebras $Λ(n,\overline{m})$, we classify the universal deformation rings of the modules lying in $Ω$-stable components $\mathfrak{C}$ of the stable Auslander-Reiten quiver provided that $\mathfrak{C}$ contains at least one simple module. Our approach uses several tools and techniques from the representation theory of Brauer graph algebras. Notably, we leverage Duffield's work on the Auslander-Reiten theory of these algebras and Opper-Zvonareva's results on derived equivalences between Brauer graph algebras.

math.RT↗

arXiv2024

On universal deformation rings of modules over a certain class of symmetric algebras of finite representation type

Let $\mathbf{k}$ be an algebraically closed field. Recently, K. Erdmann classified the symmetric $\mathbf{k}$-algebras $Λ$ of finite representation type such that every non-projective module $M$ has period dividing four. The goal of this paper is to determine the indecomposable modules $M$ over these class of algebras $Λ$ whose stable endomorphism ring is isomorphic to $\mathbf{k}$, and then calculate their corresponding universal deformation rings (in the sense of F. M. Bleher and the third author).

math.RT↗