The derived dimensions and representation distances of Artin algebras

There is a well-known class of algebras called Igusa–Todorov algebras which were introduced in relation to the finitistic dimension conjecture. As a generalization of Igusa–Todorov algebras, the new notion of (m, n)-Igusa–Todorov algebras provides a wider framework for studying derived dimensions. In this paper, we give methods for constructing (m, n)-Igusa–Todorov algebras. As an application, we present for general Artin algebras a relationship between the derived dimension and the representation distance. Moreover, we end this paper to show that the main result can be used to give a better upper bound for the derived dimension for some classes of algebras.