Igusa-Todorov and LIT algebras on Morita context algebras

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 ${\varphi }_0^{-1}(A)=\{M:\varphi (M)=0\}$ 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 $(n,V,{\varphi }_0^{-1}(A))$ 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.

arXiv admin note: text overlap with arXiv:2211.06473