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Maximal Discrete Subgroups in Unitary Groups of Operator Algebras
Vadim Alekseev, Andreas Thom TU Dresden, Institut für Geometrie, 01062 Dresden, Germany
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
Citation:
Vadim Alekseev, Andreas Thom, “Maximal Discrete Subgroups in Unitary Groups of Operator Algebras”, SIGMA, 18 (2022), 052, 7 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1848 https://www.mathnet.ru/eng/sigma/v18/p52
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Abstract page: | 54 | Full-text PDF : | 11 | References: | 16 |
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