(CA) closures of analytic groups

Zerling, David

doi:10.1090/S0002-9939-1981-0603616-0

(CA) closures of analytic groups
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by David Zerling

Proc. Amer. Math. Soc. 82 (1981), 133-138

DOI: https://doi.org/10.1090/S0002-9939-1981-0603616-0

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Abstract:

An analytic group $G$ is called $(CA)$ if the group of inner automorphisms of $G$ is closed in the Lie group of all bicontinuous automorphisms of $G$. We introduce the notion of a $(CA)$ closure for an analytic group and show that every analytic group possesses a $(CA)$ closure. The definition of uniqueness for such a $(CA)$ closure is developed and a sufficient condition for uniqueness is given. We also develop new sufficient conditions for a closed normal analytic subgroup of a $(CA)$ analytic group to be $(CA)$.

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