Triangular Lat-Igusa-Todorov algebras

TL;DR

This paper investigates the conditions under which triangular matrix algebras are Lat-Igusa-Todorov (LIT), a class of algebras satisfying the finitistic dimension conjecture, and explores their stability under tensor products.

Contribution

It provides new criteria for triangular matrix algebras to be LIT based on their component algebras and bimodules, extending the scope of LIT algebras.

Findings

Triangular matrix algebras are LIT under specific conditions related to their components.

Tensor products of LIT algebras with certain path algebras are also LIT.

The results support the broader applicability of LIT algebras in homological conjectures.

Abstract

Recently the authors D. Bravo, M. Lanzilotta, O. Mendoza and J. Vivero gave a generalization of the concept of Igusa-Todorov algebra and proved that those algebras, named Lat-Igusa-Todorov (LIT for short), satisfy the finitistic dimension conjecture. In this paper we explore the scope of that generalization and give conditions for a triangular matrix algebra to be LIT in terms of the algebras and the bimodule used in its definition. As an application we obtain that the tensor product of an LIT $\mathbb{K}$-algebra with a path algebra of a quiver whose underlying graph is a tree, is LIT.