Subalgebras, subgroups, and singularity

Abstract

AbstractThis paper is concerned with the noncommutative analog of the normal subgroup theorem for certain groups. Inspired by Kalantar and Panagopoulos (arXiv:2108.02928, 2021, 16), we show that all ‐invariant subalgebras of and are (‐)coamenable. The groups we work with satisfy a singularity phenomenon described by Bader et al. (Invent. Math. 229 (2022), 929–985). The setup of singularity allows us to obtain a description of ‐invariant intermediate von Neumann subalgebras in terms of the normal subgroups of .