Maximal discrete subgroups in unitary groups of operator algebras
arXiv:2206.06704 · doi:10.3842/SIGMA.2022.052
Abstract
We show that if a group G is mixed-identity-free, then the projective unitary group of its group von Neumann algebra contains a maximal discrete subgroup containing G. The proofs are elementary and make use of free probability theory. In addition, we clarify the situation for C*-algebras.
9 pages