Igusa-Todorov and LIT algebras on Morita context algebras

TL;DR

This paper investigates how Igusa-Todorov and LIT algebra properties are preserved under Morita context constructions, establishing conditions for these properties to hold and exploring their behavior in opposite algebras.

Contribution

It proves that Morita context algebras from Igusa-Todorov and LIT algebras with zero bimodule morphisms are also Igusa-Todorov or LIT, under certain conditions.

Findings

Morita context algebras inherit Igusa-Todorov or LIT properties under specific conditions.

The class ^{-1}(A) is a 0-Igusa-Todorov subcategory iff A is selfinjective or has finite global dimension.

Opposite algebra of a LIT algebra is generally not LIT.

Abstract

In this article, we prove that, under certain conditions, Morita context algebras that arise from Igusa-Todorov (LIT) algebras and have zero bimodule morphisms are also Igusa-Todorov (LIT). For a finite dimensional algebra $A$, we prove that the class $\phi_0^{-1}(A) = \{M: \phi(M)=0\}$ is a 0-Igusa-Todorov subcategory if and only if $A$ is selfinjective or gl$\dim l(A)< \infty$. As a consequence $A$ is an $(n,V, \phi_0^{-1}(A))$ algebra if and only if $A$ is selfinjective or gl$\dim(A)< \infty$. We also show that the opposite algebra of a LIT algebra is not LIT in general.