The derived dimensions of $(m,n)$-Igusa-Todorov algebras

TL;DR

This paper establishes an upper bound for the dimension of bounded derived categories of $(m,n)$-Igusa-Todorov algebras, generalizing previous concepts and linking it to projective dimensions and radical layer length.

Contribution

It introduces a new upper bound for derived category dimensions of $(m,n)$-Igusa-Todorov algebras, extending the theory beyond $n$-Igusa-Todorov algebras.

Findings

Derived upper bounds for derived category dimensions.

Connection between algebraic invariants and derived category complexity.

Generalization of existing bounds to broader class of algebras.

Abstract

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 upper bound for the dimension of bounded derived categories in terms of the projective dimensions of certain of simple modules as well as radical layer length of artin algebra $\Lambda$.