Work

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

Year: 2025

Type: article

Abstract: We prove that every locally compact second countable group G arises as the outer automorphism group $\operatorname{Out} M$ 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 $\operatorname{Out} M$ .

Source: Proceedings of the Royal Society of Edinburgh Section A Mathematics

DOI: 10.1017/prm.2025.25

Author: Stefaan Vaes

Institution: KU Leuven

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4408945991

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Cites: 9

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Related to: 10