Igusa-Todorov dimensions and derived dimensions of artin algebras

Abstract

We introduce the notion of Igusa-Todorov dimension, and prove that this dimension is an invariant under derived equivalent. Igusa-Todorov dimension also give a characterization of Igusa-Todorov algebras, and in fact that an artin algebra is an Igusa-Todorov algebra if and only if its Igusa-Todorov dimension at most 1. We point out some artin algebras having Igusa-Todorov dimension more than one. We also give a new upper bound for the derived dimension of (m, n)-Igusa-Todorv algebra.