Related papers: Igusa-Todorov functions for radical square zero al…

We define the Igusa-Todorov function in the context of finite dimensional comodules and prove that a coalgebra is left qcF if and only if it is left semiperfect and its Igusa-Todorov function on each right finite dimensional comodule is…

In this survey, we review the fundamental properties of the Igusa-Todorov functions, the $\phi$-dimension, the $\psi$-dimension and their generalizations.

K. Igusa and G. Todorov introduced two functions $\phi$ and $\psi,$ which are natural and important homological measures generalising the notion of the projective dimension. These Igusa-Todorov functions have become into a powerful tool to…

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 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…

Given a truncated path algebra $A=\frac{\Bbbk Q}{J^k}$ we prove that $\fidim A = \fidim A^{\op}$. We also compute the $\phi$-dimension of $A$ in function of the $\phi$-dimension of $\frac{\Bbbk Q}{J^2}$ when $Q$ has no sources nor sinks.…

For a finite dimensional algebra $A$ with $0 < \phi dim (A) = m < \infty$ we prove that there always exist modules $M$ and $N$ such that $\phi(M) = m-1$ and $\phi (N) = 1$. On the other hand, we see an example of an algebra that not every…

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…

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 paper studies entire functions of finite order of growth for which a representation of the form $\psi(z) = 1+ O(|z|^{-\mu}), \mu >0,$ as $z\to \infty$, is valid on a fixed ray of the complex plane. The main result is the following.…

In a previous paper, dealing with "Applications in $\mathbb{R}^1$," the authors developed a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS and studied some applications…

In this paper we study the operator inequality \phi(X)\leq X and the operator equation \phi(X)= X, where \phi is a w^*-continuous positive (resp. completely positive) linear map on B(H). We show that their solutions are in one-to-one…

By constructing new quasimap compactifications of Hurwitz spaces of degrees 4 and 5, we establish a new connection between arithmetic statistics, quantum algebra, and geometry and answer a question of Ellenberg-Tran-Westerland and…

A classical result in the theory of Hopf algebras concerns the uniqueness and existence of integrals: for an arbitrary Hopf algebra, the integral space has dimension $\leq 1$, and for a finite dimensional Hopf algebra, this dimension is…

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…

Symmetries corresponding to local transformations of the fundamental fields that leave the action invariant give rise to (invertible) topological defects, which obey group-like fusion rules. One can construct more general (codimension-one)…

In this paper, we analyze carefully the behaviour in $L^\infty(\mathbb R)$ of the square functions $S$ and $S_\mathcal I$'s, originating from ergodic theory. Firstly, we show that we can find some function $f\in L^\infty(\mathbb{R})$, such…

We study symmetries enjoyed by the polynomials enumerating non-degenerate flags in finite vector spaces, equipped with a non-degenerate alternating bilinear, hermitian or quadratic form. To this end we introduce Igusa-type rational…

We study the boundary behavior of functions in the Hardy spaces on the infinite dimensional polydisk. These spaces are intimately related to the Hardy spaces of Dirichlet series. We exhibit several Fatou and Marcinkiewicz-Zygmund type…

We investigate linear operators between C$^\ast$-algebras which approximately preserve involution and orthogonality, the latter meaning that for some $\varepsilon>0$ we have $\|\phi(x)\phi(y)\|\leq\varepsilon\|x\|\|y\|$ for all positive…