Topologically Conjugate Classifications of the Translation Actions on Compact Connected Lie Groups $\mathrm{SU}(2)\times T^n$

Abstract

In this article, we focus on the left (translation) actions on noncommutative compact connected Lie groups $\mathrm{SU}(2)\times T^n$. We define the rotation vectors of the left actions induced by the elements in the maximal tori of $\mathrm{SU}(2)\times T^n$, and utilize rotation vectors to give the complete topologically conjugate classifications of left actions. Algebraic conjugacy and smooth conjugacy are also considered.

42 pages