The classification of tilting modules over Harada algebras
The classification of tilting modules over Harada algebras
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DOI：
10.2969/jmsj/06441333
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发表时间：
2009-05
期刊：
影响因子：
--
通讯作者：
K. Yamaura
中科院分区：
文献类型：
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作者：
K. Yamaura
在20世纪80年代，Harada引入了一类新的代数，现在称为Harada代数。Harada代数为我们提供了Auslander的1-Gorenstein代数的丰富来源。在本文中，我们得到了关于Harada代数的两个主要结果。第一个问题是射影维数至多为1的Harada代数上的模的分类。第二是Harada代数上的倾斜模的分类，给出了Harada代数上的倾斜模和$K上的上三角矩阵代数直积上的倾斜模之间的双射。已知$K$上三角矩阵代数上倾斜模的一个组合刻画。这些事实允许我们对给定的Harada代数上的倾斜模进行分类。
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.