Dynamic Asymptotic Dimension of Translation Actions on Compact Lie\n Groups

2020/11/14 by Samantha Pilgrim, Pilgrim, Samantha
Computer Science · Mathematics · #20F65 (secondary) #37B99 (primary) #47L65 (secondary) #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Operator Algebras (math.OA) #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2011.07395

openalex publication_date 2020/11/14 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We develop a method to bound the dynamic asymptotic dimension of isometric\ngroup actions \Γ curvearrowright X in terms of the asymptotic dimension\nof a space of graphs similar to a box space of \Γ (which also determines\nfinite-dimensionality), and a geometric property of X related to the doubling\ndimension. We apply this method to describe the DAD of translation actions by\nfinitely generated subgroups of compact Lie groups, characterize finite\ndimensionality of such actions, and consequently bound the nuclear dimension of\nC^*-algebras arising from such actions by amenable groups.\n

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