Splitting in orbit equivalence, treeable groups, and the Haagerup property
Splitting in orbit equivalence, treeable groups, and the Haagerup property
<!-- *** Custom HTML *** --> Let $G$ be a discrete countable group and $C$ its central subgroup with $G/C$ treeable. We show that for any treeable action of $G/C$ on a standard probability space $X$, the groupoid $G\ltimes X$ is isomorphic to the direct product of $C$ and $(G/C)\ltimes …