2023/09/13 by Zhijing Wendy Wang, Wang, Zhijing Wendy
Mathematics · #37A17 #37C79(Primary) #37D30 #Advanced Algebra and Geometry #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2309.07282
openalex publication_date 2023/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove centralizer rigidity near an element of the Weyl chamber flow on a semisimple Lie group. We show that a volume preserving perturbation of an element of the Weyl chamber flow on a quotient G/Γ of an ℝ-split, simple Lie group G either has centralizer of dimension 0 or 1, or is smoothly conjugate to an element of the Weyl chamber flow. We also acquire a general condition for the centralizer of a partially hyperbolic diffeomorphism to be a Lie group.