The classification of tilting modules over Harada algebras

Abstract

In the 1980s, Harada introduced a class of algebras now called Harada algebras. The aim of this paper is to study Harada algebras in representation theoretical point of view. The paper concludes the following two results. The first is the classification of modules over left Harada algebras whose projective dimension is at most one. The second is the classification of tilting modules over left Harada algebras, which is done by giving a bijection between tilting modules over Harada algebras and tilting modules over direct products of upper triangular matrix algebras over a field.