Every locally compact group is the outer automorphism group of a II₁ factor

2024/03/29 by Stefaan Vaes, Vaes, Stefaan
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2403.20299

openalex publication_date 2024/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every locally compact second countable group G arises as the outer automorphism group Out M of a II₁ factor, which was so far only known for totally disconnected groups, compact groups and a few isolated examples. We obtain this result by proving that every locally compact second countable group is a centralizer group, a class of Polish groups that arise naturally in ergodic theory and that may all be realized as Out M.

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