|
| 摘要: |
| 设Fq为有限域，（n1，n2，…，nr）为一正整数序列，B（q，r）为由Fq上对角块为ni（1 ≤ i ≤ r）阶方阵的分块上三角阵构成的代数.理想包含图In（B（q，r））是一个有向图，它以B（q，r）为顶点集，从A到B有一条有向边当且仅当IA⫋IB，其中IA表示A生成的双边理想.本文研究了理想包含图In（B（q，r））上自同构的刻画问题.通过研究B（q，r）中理想的形式，在此基础上对给定的自同构构造一些标准自同构，使得复合后的自同构固定所有的顶点，从而给出了任意自同构的具体描述，推广了文献[13]的结果. |
| 关键词: 理想包含图 图的自同构 分块上三角矩阵 理想 |
| DOI： |
| 分类号:O157.5 |
| 基金项目:国家自然基金资助（11571360）. |
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| AUTOMORPHISMS OF INCLUSION IDEAL GRAPHS OVER BLOCK UPPER TRIANGULAR MATRICES |
|
CHEN Li
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| Abstract: |
| Let Fq be a finite field and (n1, n2,…, nr) a sequence of positive integers. The algebra B(q, r) consists of all block upper triangular matrices over Fq with an ni×ni square matrix as i-diagonal block (1 ≤ i ≤ r). The inclusion ideal graph In(B(q, r)) is defined as a directed graph whose vertex set is B(q, r) and there is a directed edge from A to B if and only if IA⫋IB where IA denotes the two-sided ideal generated by A. In this paper, we investigate the characterization of the automorphisms of In(B(q, r)). We first investigate the ideals of In(B(q, r)), then for any given automorphism of In(B(q, r)), by constructing some standard automorphisms such that the composition of these automorphisms fixes all vertices, we give a explicit description of the given automorphism, which extends the result of the reference[13]. |
| Key words: inclusion ideal graph graph automorphism block upper triangular matrix ideal |
