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• W3193647755 endingPage "108894" @default.
• W3193647755 startingPage "108894" @default.
• W3193647755 abstract "We show that the commutator subgroup of the group of unitaries connected to the identity in a simple unital C*-algebra is simple modulo its center. We then go on to investigate the role of “regularity properties” in the structure of the special unitary group of a C*-algebra. Under mild assumptions, we show that this group has the invariant automatic continuity property and a unique polish group topology. Strengthening our assumptions in the case of simple C*-algebras, we show that the special unitary group modulo its center has bounded normal generation. These results apply to all simple purely infinite C*-algebras and to all simple nuclear C*-algebras in the “classifiable class”. We show with counterexamples how our conclusions may in general fail if no regularity conditions are imposed on the C*-algebra." @default.
• W3193647755 created "2021-08-30" @default.
• W3193647755 creator A5045947995 @default.
• W3193647755 creator A5090429630 @default.
• W3193647755 date "2023-02-01" @default.
• W3193647755 modified "2023-09-23" @default.
• W3193647755 title "Simplicity, bounded normal generation, and automatic continuity of groups of unitaries" @default.
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• W3193647755 doi "https://doi.org/10.1016/j.aim.2023.108894" @default.
• W3193647755 hasPublicationYear "2023" @default.
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