Von Neumann Dimensions and Trace Formulas II: A Jacquet-Langlands correspondence for Arithmetic Group Algebras in $\mathrm{GL}(2)$

Jun Yang

We propose a global Jacquet-Langlands correspondence for the modules over the von Neumann algebras of $S$-arithmetic subgroups of $\mathrm{GL}(2)$ and of a quaternion algebra $D$, whic…