Structure of Quasi-Invariant Vector Spaces

Abstract:

      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.