Every locally compact group is the outer automorphism group of a II$_1$ factor

Autor:	Vaes, Stefaan
Rok vydání:	2024
Předmět:	Mathematics - Group Theory Mathematics - Dynamical Systems Mathematics - Operator Algebras
Druh dokumentu:	Working Paper
Popis:	We prove that every locally compact second countable group $G$ arises as the outer automorphism group Out $M$ of a II$_1$ 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 $M$. Comment: v2: minor changes, with a few extra details added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.20299 Zobrazit plný text záznamu View this record from Arxiv