Maximal Discrete Subgroups in Unitary Groups of Operator Algebras - Alekseev, Vadim; Thom, Andreas (Symmetry, Integrability and Geometry: Methods and Applications, 2022)
We show that if a group is mixed-identity-free, then the projective unitary group of its group von Neumann algebra contains a maximal discrete subgroup containing . The proofs are elementary and utilize free probability theory. In addition, we clarify the situation for *-algebras.