The classification of tilting modules over Harada algebras

Details The classification of tilting modules over Harada algebras The classification of tilting modules over Harada algebras

2009-05-14

arxiv.org/abs/0905.2245v2

Mathematics

Rings and Algebras

15 pages

Scientific paper

In the 1980s, Harada introduced a new class of algebras now called Harada algebras. Harada algebras provides us with a rich source of Auslander's 1-Gorenstein algebras. In this paper, we have two main results about Harada algebras. The first is the classification of modules over Harada algebras whose projective dimension is at most one. The second is the classification of tilting modules over Harada algebras, which is shown by giving a bijection between tilting modules over Harada algebras and tilting modules over direct products of upper triangular matrix algebras over $K$. A combinatorial description of tilting modules over upper triangular matrix algebras over $K$ is known. These facts allow us to classify tilting modules over a given Harada algebra.

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