Topologically conjugate classifications of the translation actions on low-dimensional compact connected Lie groups  

作　　者：Xiaotian Pan Bingzhe Hou 

机构地区：[1]School of Mathematics,Jilin University,Changchun 130012,China

出　　处：《Science China Mathematics》2021年第5期963-1010,共48页中国科学：数学（英文版）

摘　　要：In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of SU(2), U(2), SO(3), SO(3)×S^(1) and Spin ^(C)(3). We define the rotation vectors(numbers) of the left actions induced by the elements in the maximal tori of these groups, and utilize rotation vectors(numbers) to give the topologically conjugate classification of the left actions. Algebraic conjugacy and smooth conjugacy are also considered. As a by-product, we show that for any homeomorphism f : L(p,-1) × S^(1)→ L(p,-1) × S^(1), the induced isomorphism(π■f■i)_(*) maps each element in the fundamental group of L(p,-1) to itself or its inverse, where i : L(p,-1) → L(p,-1) × S^(1) is the natural inclusion and π : L(p,-1) × S^(1)→ L(p,-1) is the projection.

关 键 词：topological conjugacy rotation vectors translation actions C~*-dynamical system classification 

分 类 号：O152.5[理学—数学]