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Symmetry, Integrability and Geometry: Methods and Applications, 2022, Volume 18, 052, 7 pp.
DOI: https://doi.org/10.3842/SIGMA.2022.052 (Mi sigma1848) 		 
Maximal Discrete Subgroups in Unitary Groups of Operator Algebras

Vadim Alekseev, Andreas Thom

TU Dresden, Institut für Geometrie, 01062 Dresden, Germany
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DOI: https://doi.org/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.
Keywords: maximal discrete subgroups, unitary groups, operator algebras.
Received: February 22, 2022; in final form June 29, 2022; Published online July 9, 2022
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Document Type: Article
MSC: 46L10, 22E40, 20F38
Language: English
Citation: Vadim Alekseev, Andreas Thom, “Maximal Discrete Subgroups in Unitary Groups of Operator Algebras”, SIGMA, 18 (2022), 052, 7 pp.
Citation in format AMSBIB
\Bibitem{AleTho22}
\by Vadim~Alekseev, Andreas~Thom
\paper Maximal Discrete Subgroups in Unitary Groups of Operator Algebras
\jour SIGMA
\yr 2022
\vol 18
\papernumber 052
\totalpages 7
\mathnet{http://mi.mathnet.ru/sigma1848}
\crossref{https://doi.org/10.3842/SIGMA.2022.052}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4449420}
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