向量空间中拟不变元素的结构(英文)

Structure of Quasi-Invariant Vector Spaces

英文关键词:vector space  quasi-invariant.

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.