Igusa-Todorov functions for Artin algebras

TL;DR

This paper investigates the properties of Igusa-Todorov functions for Artin algebras with finite injective dimension, demonstrating finiteness of these functions for various algebra classes including Gorenstein, monomial, gentle, and cluster tilted algebras.

Contribution

It establishes the finiteness of Igusa-Todorov functions for specific classes of Artin algebras, extending understanding of their homological behavior.

Findings

The $$-dimension and $$-dimension are finite for Artin algebras with finite injective dimension.

Monomial, gentle, and cluster tilted algebras have finite $$-dimension and $$-dimension.

The results apply to Gorenstein algebras as a particular case.

Abstract

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 both cases. Also we prove that monomial, gentle and cluster tilted algebras have finite $\phi$-dimension and finite $\psi$-dimension.