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arXiv · 2206.06704

Maximal discrete subgroups in unitary groups of operator algebras

Vadim Alekseev·Andreas Thom
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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.

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Vadim Alekseev, Andreas Thom. 2022-06-14. Maximal discrete subgroups in unitary groups of operator algebras. https://doi.org/10.3842/sigma.2022.052

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