arXiv subjects

G. Mata

Publications and source records attributed to G. Mata.

3 recordsLinked to original sources

arXiv2026

Bounds on Frobenius dimension

In this article, we prove two types of results about the Frobenius dimension of associative algebras. First, we refine the known upper bound for the Frobenius dimension of a finite dimensional algebra in terms of its dimension as a vector space, and show that the only algebras reaching this bound are radical square zero algebras associated with single-vertex quivers. Second, we compute Frobenius dimension for low-dimensional algebras explicitly, and for truncated path algebras in terms of paths with no detours in their underlying quivers.

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arXiv2023

Igusa-Todorov and LIT algebras on Morita context algebras

In this article, we prove that, under certain conditions, Morita context algebras that arise from Igusa-Todorov (LIT) algebras and have zero bimodule morphisms are also Igusa-Todorov (LIT). For a finite dimensional algebra $A$, we prove that the class $\phi_0^{-1}(A) = \{M: \phi(M)=0\}$ is a 0-Igusa-Todorov subcategory if and only if $A$ is selfinjective or gl$\dim l(A)< \infty$. As a consequence $A$ is an $(n,V, \phi_0^{-1}(A))$ algebra if and only if $A$ is selfinjective or gl$\dim(A)< \infty$. We also show that the opposite algebra of a LIT algebra is not LIT in general.

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arXiv2015

Igusa-Todorov functions for radical square zero algebras

We study the behaviour of the Igusa-Todorov functions for radical square zero algebras. We show that the left and the right $ϕ$-dimensions coincide, in this case. Some general results are given, but we concentrate more in the radical square zero algebras. Our study is based on two notions of hearth and member of a quiver $Q$. We give some bounds for the $ϕ$ and the $ψ$-dimensions and we describe the algebras for which the bound of $ψ$ is obtained. We also exhibit modules for which the $ϕ$-dimension is realised.

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