On fullness of von Neumann algebras associated with non-singular Borel equivalence relations

TL;DR

This paper extends the understanding of fullness in von Neumann algebras associated with non-singular Borel equivalence relations, showing that bi-exact locally compact groups produce full factors under certain conditions.

Contribution

It generalizes Houdayer-Isono's result from countable discrete groups to bi-exact locally compact groups, broadening the class of groups for which fullness is established.

Findings

Fullness of von Neumann algebras for bi-exact locally compact groups

Extension of Houdayer-Isono's results to broader group classes

Verification of fullness under strong ergodicity and non-singularity

Abstract

It is shown by Houdayer-Isono that a group measure space von Neumann algebra is a full factor if the group is countable discrete and bi-exact, and the action is strongly ergodic, essentially free and non-singular. Recently, bi-exactness for locally compact groups was introduced by Brothier-Deprez-Vaes. In this paper, we will show that Houdayer-Isono type result holds for bi-exact locally compact groups.