冯红.向量空间中拟不变元素的结构(英文)[J].数学研究及应用,2000,20(2):197~200 |
向量空间中拟不变元素的结构(英文) |
Structure of Quasi-Invariant Vector Spaces |
投稿时间:1997-07-04 |
DOI:10.3770/j.issn:1000-341X.2000.02.008 |
中文关键词: |
英文关键词:vector space quasi-invariant. |
基金项目: |
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中文摘要: |
设V是有限域上F的向量空间,G是V上的线性变换群.本文讨论了V中拟不变元素的结构·即如果U是V中的拟不变元,则存在g∈G,使得U∩g(U)是G-不变的,或存在x∈ V\U,使得 V+是 G不变的. |
英文摘要: |
Let V be a vector space over a field F and G a group of linear transformations in V. It is proved in this note that for any subspace U?V, if dim U/(U∩g(U))≤ 1, for any g∈G, then there is a g∈ G such that U∩g(U) is a G-invariant subspace, or there is an x∈V\U such that U+ is a G-invariant subspace. So a vector-space analog of Brailovsky's results on quasi-invariant sets is given. |
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