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Viviana Gubitosi

Publications and source records attributed to Viviana Gubitosi.

13 recordsLinked to original sources
arXiv2026

The coloured mutation class of $\mathbb{D}_n$- quivers and their application to $m$-cluster tilted algebras

In this paper, we present an explicit and purely combinatorial characterization of the $m$-coloured quivers that appear within the $m$-coloured mutation class of a quiver of type $\mathbb{D}_n$. The $m$-coloured mutation, as defined by Buan and Thomas in \cite{BT}, generalises the well-known quiver mutation introduced by Fomin and Zelevinsky \cite{FZ}. Consequently, we derive a comprehensive description of the Gabriel quivers associated with $m$-cluster-tilted algebras of type $\mathbb{D}_n$. Notably, our characterization extends a result by Vatne, \cite{Va}, which we recover when $m=1$.

math.RT↗
arXiv2026

Some remarks about $FP_{n}$-projective and $FP_{n}$-injective modules

Let $R$ be a ring. In \cite{MD4} Mao and Ding defined an special class of $R$-modules that they called \( FP_n \)-projective $R$-modules. In this paper, we give some new characterizations of \( FP_n \)-projective $R$-modules and strong $n$-coherent rings. Some known results are extended and some new characterizations of the \( FP_n \)-injective global dimension in terms of \( FP_n \)-projective $R$-modules are obtained. Using the \( FP_n \)-projective dimension of an $R$-module defined by Ouyang, Duan and Li in \cite{Ouy} we introduce a slightly different \( FP_n \)-projective global dimension over the ring $R$ which measures how far away the ring is from being Noetherian. This dimension agrees with the $(n,0)$-projective global dimension of \cite{Ouy} when the ring in question is strong $n$-coherent.

math.RA↗
arXiv2025

An explicit description of the colored mutation class of $\widetilde{\mathbb{A}}_n$-quivers

This paper addresses the combinatorial structure of $m$-colored mutation classes. We provide an explicit and purely combinatorial description of the $m$-colored quivers that arise within the $m$-colored mutation class of a quiver of type $\mathbb{\widetilde{A}}$. Our results generalize and extend existing work, specifically recovering a description by Bastian [1] when the case $m=1$ is considered.

math.CO↗
arXiv2025

Algebras determined by $τ$-slices

In this paper we revisit the notion of strict laura algebras through the lens of $τ$-tilting theory to define the family of algebras determined by $τ$-slices. We show that the representation dimension of every algebra determined by $τ$-slices satisfying mild conditions is at most three.

math.RA↗
arXiv2023

The coloured mutation class of $\mathbb{A}_n$ quivers

In this paper we give an explicit and pure combinatorial description of the $m$-coloured quivers that appears in the $m$-coloured mutation class of a quiver of type $\mathbb{A}_n$. The $m$-coloured mutation defined by Buan and Thomas in \cite{BT} generalizes the well-known quiver mutation of Fomin and Zelevinsky \cite{FZ}. In particular, our description generalizes a result of Buan and Vatne, \cite{BV}, which we recover when $m=1$.

math.RT↗
arXiv2023

On the non-existence of perfect codes in the Niederreiter-Rosenbloom-Tsfasman metric

In this paper we consider codes in $\mathbb{F}_q^{s\times r}$ with packing radius $R$ regarding the NRT-metric (i.e. when the underlying poset is a disjoint union of chains with the same length) and we establish necessary condition on the parameters $s,r$ and $R$ for the existence of perfect codes. More explicitly, for $r,s\geq 2$ and $R\geq 1$ we prove that if there is a non-trivial perfect code then $(r+1)(R+1)\leq rs$. We also explore a connection to the knapsack problem and establish a correspondence between perfect codes with $r>R$ and those with $r=R$. Using this correspondence we prove the non-existence of non-trivial perfect codes also for $s=R+2$.

math.CO↗
arXiv2022

Finiteness properties and homological dimensions of Skew Group rings

Let $G$ be a finite group acting on a ring $R$ and $H$ a subgroup of $G$. In this paper we compare some homological dimensions over the skew group rings $RG$ and $RH$. Moreover, under the assumption that $RG$ is a separable extension over $RH$, we show that the skew group rings $RG$ and $RH$ share some properties such as being $n$-Gorenstein, $n$-perfect, $n$-coherent, $(n,d)$, Ding-Chen or IF-rings.

math.RA↗
arXiv2022

Open Frobenius cluster tilted algebras

In this paper, we compute the Frobenius dimension of any cluster tilted algebra of finite type. Moreover, we give conditions on the bounded quiver of a cluster tilted algebra $Λ$ such that $Λ$ has non-trivial open Frobenius structures.

math.RT↗
arXiv2020

Repetitive cluster categories of type Dn

In this paper, we show that the repetitive cluster category of type $D_n$, defined as the orbit category $\mathcal{D}^b(\mathrm{mod}K D_n)/(τ^{-1}[1])^p$, is equivalent to a category defined on a subset of tagged edges in a regular punctured polygon. This generalizes the construction of Schiffler, \cite{S}, which we recover when $p=1$.

math.RT↗
arXiv2019

Hochschild cohomology of $m$-Cluster tilted algebras of type $\widetilde{\mathbb{A}}$

In this paper, we compute the dimension of the Hochschild cohomology groups of any $m$-cluster tilted algebra of type $\tilde{\mathbb{A}}$. Moreover, we give conditions on the bounded quiver of an $m$-cluster tilted algebra $Λ$ of type $\tilde{\mathbb{A}}$ such that the Gerstenhaber algebra $\operatorname{HH}^*(Λ)$ has non-trivial multiplicative structures. We also show that the derived class of gentle $m$-cluster tilted algebras is not always completely determined by the Hochschild cohomology.

math.RA↗
arXiv2015

M-cluster tilted algebras of type A tilde

In this paper, we characterize all the finite dimensional algebras that are m-cluster tilted algebras of type A tilde. We show that these algebras are gentle and we give an explicit description of their quivers with relations.

math.RT↗