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

Topologically conjugate classifications of the translation actions on compact connected Lie groups SU(2) × T n