Related papers: Igusa-Todorov distances
We introduce Igsua-Todorov distances of Artin algebra, prove its invariance under derived equivalence, present its application to exterior algebra, and establish the link between the dimension of the singularity category and this distance.
There is a well-known class of algebras called Igusa-Todorov algebras which were introduced in relation to finitistic dimension conjecture. As a generalization of Igusa-Todorov algebras, the new notion of $(m,n)$-Igusa-Todorov algebras…
In this paper we study a generalisation of the Igusa-Todorov functions which gives rise to a vast class of algebras satisfying the finitistic dimension conjecture. This class of algebras is called Lat-Igusa-Todorov and includes, among…
We give an upper bound for the dimension of the bounded derived categories of $(m,n)$-Igusa-Todorov algebras which is a generalization of $n$-Igusa-Todorov algebras, where $m,n$ are two nonnegative integers. As an applications, we get a new…
In this paper, we investigate the behavior of Igusa-Todorov properties under recollements of abelian categories. In particular, we study how the Igusa-Todorov distances of the categories involved in a recollement are related. Applications…
Let $A$ be an Artin algebra and $F$ a non-zero subfunctor of $\Ext_A^{1}(-,-)$. In this paper, we characterize the relative $\phi$-dimension of $A$ by the bi-functor $\Ext_F^1(-,-)$. Furthermore, we show that the finiteness of relative…
The extension dimensions of an Artin algebra give a reasonable way of measuring how far an algebra is from being representation-finite. In this paper we mainly study extension dimensions linked by recollements of derived module categories…
In [8] V. G\'elinas introduced a homological invariant, called {\it delooping level} (dell), that bounds the finitistic dimension. In this article, we introduce another homological invariant (Dell) related to the delooping level for an…
A new homological dimension is introduced to measure the quality of resolutions of `singular' finite dimensional algebras (of infinite global dimension) by `regular' ones (of finite global dimension). Upper bounds are established in terms…
We develope the theory of the $\mathcal{E}$-relative Igusa-Todorov functions in an exact $ IT$-context $(\mathcal{C},\mathcal{E}).$ In the case when $\mathcal{C}=$mod$\, (\Lambda)$ is the category of finitely generated left…
In this article we prove that, under certain hypotheses, Morita context algebras that have zero bimodule morphisms have finite $\phi$-dimension. We also study the behaviour of the $\phi$-dimension for an algebra and its opposite. In…
In this paper we study the behaviour of the Igusa-Todorov functions for Artin algebras A with finite injective dimension, and Gorenstein algebras as a particular case. We show that the $\phi$-dimension and $\psi$-dimension are finite in…
Lat-Igusa-Todorov algebras are a natural generalization of Igusa-Todorov algebras. They are defined using the generalized Igusa-Todorov functions given in \cite{BLMV} and also verify the finitistic dimension conjecture. In this article we…
The notion of Igusa-Todorov classes is introduced in connection with the finitistic dimension conjecture. As application we consider conditions on special ideals which imply the Igusa-Todorov and other finiteness conditions on modules…
The Gromov-Hausdorff distance is a dissimilarity metric capturing how far two spaces are from being isometric. The Gromov-Prokhorov distance is a similar notion for metric measure spaces. In this paper, we study the topological dimension of…
The Gromov--Hausdorff distance (hereinafter referred to as the GH-distance) is a measure of non-isometricity of metric spaces. In this paper, we study a modification of this distance that also takes topological differences into account. The…
Using the Rost invariant for non split simply connected groups, we define a relative degree $3$ cohomological invariant for pairs of orthogonal or unitary involutions having isomorphic Clifford or discriminant algebras. The main purpose of…
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…
In this paper, we investigate the behavior of Igusa-Todorov distances, extension and Rouquier dimensions under cleft extensions of abelian categories. We apply our results to Morita context rings, trivial extension rings, tensor rings and…
We show that the difference of the extension dimensions of two derived equivalent algebras is bounded above by the minimal length of a tilting complex associated with a derived equivalence, and that the extension dimension is an invariant…