Maximal Discrete Subgroups in Unitary Groups of Operator Algebras

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2022
• ISSN: 1815-0659
• Main Authors: Alekseev, Vadim, Thom, Andreas
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2022
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211735
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Maximal Discrete Subgroups in Unitary Groups of Operator Algebras. Vadim Alekseev and Andreas Thom. SIGMA 18 (2022), 052, 7 pages

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.