E-resources
Open access
-
Chifan, Ionut; Das, Sayan; Sun, Bin
arXiv (Cornell University), 02/2023Paper, Journal Article
Using an interplay between geometric methods in group theory and soft von Neuman algebraic techniques we prove that for any icc, acylindrically hyperbolic group \(\Gamma\) its von Neumann algebra \(L(\Gamma)\) satisfies the so-called ISR property: \emph{any von Neumann subalgebra \(N\subseteq L(\Gamma)\) that is normalized by all group elements in \(\Gamma\) is of the form \(N= L(\Sigma)\) for a normal subgroup \(\Sigma \lhd \Gamma\).} In particular, this applies to all groups \(\Gamma\) in each of the following classes: all icc (relatively) hyperbolic groups, most mapping class groups of surfaces, all outer automorphisms of free groups with at least three generators, most graph product groups arising from simple graphs without visual splitting, etc. This result answers positively an open question of Amrutam and Jiang from \cite{AJ22}. In the second part of the paper we obtain similar results for factors associated with groups that admit nontrivial (quasi)cohomology valued into various natural representations. In particular, we establish the ISR property for all icc, nonamenable groups that have positive first \(L^2\)-Betti number and contain an infinite amenable subgroup.
![loading ... loading ...](themes/default/img/ajax-loading.gif)
Shelf entry
Permalink
- URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year | Impact factor | Edition | Category | Classification | ||||
---|---|---|---|---|---|---|---|---|
JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
Select the library membership card:
If the library membership card is not in the list,
add a new one.
DRS, in which the journal is indexed
Database name | Field | Year |
---|
Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
---|
Source: Personal bibliographies
and: SICRIS
The material is available in full text. If you wish to order the material anyway, click the Continue button.