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- W2963202247 abstract "Abstract We investigate the normal subgroups of the groups of invertibles and unitaries in the connected component of the identity of a {mathrm{C}^{*}} -algebra. By relating normal subgroups to closed two-sided ideals we obtain a “sandwich condition” describing all the closed normal subgroups both in the invertible and in the unitary case. We use this to prove a conjecture by Elliott and Rørdam: in a simple mathrm{C}^{*} -algebra, the group of approximately inner automorphisms induced by unitaries in the connected component of the identity is topologically simple. Turning to non-closed subgroups, we show, among other things, that in a simple unital mathrm{C}^{*} -algebra the commutator subgroup of the group of invertibles in the connected component of the identity is a simple group modulo its center. A similar result holds for unitaries under a mild extra assumption." @default.
- W2963202247 created "2019-07-30" @default.
- W2963202247 creator A5045947995 @default.
- W2963202247 date "2019-11-01" @default.
- W2963202247 modified "2023-10-14" @default.
- W2963202247 title "Normal subgroups of invertibles and of unitaries in a C*-algebra" @default.
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- W2963202247 doi "https://doi.org/10.1515/crelle-2017-0020" @default.
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