A note on type I groups acting on d-regular trees

2015/06/09 by Corina Ciobotaru, Ciobotaru, Corina
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1506.02950

openalex publication_date 2015/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we give new examples of type I groups generalizing a previous result of Ol'shanskii. More precisely, we prove that all closed non-compact subgroups of Aut(T_d) acting transitively on the vertices and on the boundary of a d-regular tree and satisfying Tits' independence property are type I groups. We claim no originality as we use standard ingredients: the polar decomposition of those groups and the admissibility of all their irreducible unitary representations.

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