On the algebraic structure of the unitary group

2006/04/11 by Éric Ricard, Eric Ricard, Ricard, Eric +2 · 1 citation
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.FA #math.GR

paper · pdf · doi:10.48550/arxiv.math/0604250

arxiv created 2006/04/11 · openalex publication_date 2006/04/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the unitary group \U of complex, separable, infinite-dimensional Hilbert space as a discrete group. It is proved that, whenever \U acts by isometries on a metric space, every orbit is bounded. Equivalently, \U is not the union of a countable chain of proper subgroups, and whenever \E⊆ \U generates \U, it does so by words of a fixed finite length.

Citations

• A topological version of the Bergman property

Cited by

• Projective simplicity and Bergman's property for unit groups of continuous rings

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