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(CA) closures of analytic groups

Author: David Zerling
Journal: Proc. Amer. Math. Soc. 82 (1981), 133-138
MSC: Primary 22E05
MathSciNet review: 603616
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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)$.

References [Enhancements On Off] (What's this?)

  • [1] M. Goto, Analytic subgroups of $ GL(n,R)$, Tôhoku Math. J. (2) 25 (1973), 197-199. MR 0322099 (48:463)
  • [2] -, Immersions of Lie groups, J. Math. Soc. Japan (to appear). MR 589110 (82c:22011)
  • [3] T. C. Stevens, Weakened topology for Lie groups, Ph. D. Thesis, Dept. of Math., Harvard Univ., Cambridge, Mass., 1978.
  • [4] W. T. van Est, Dense imbeddings of Lie groups, Indag. Math. 14 (1952), 255-274.
  • [5] -, Some theorems on $ ({\text{CA)}}$ Lie algebras. I, II, Indag. Math. 14 (1952), 546-568.
  • [6] D. Zerling, Some theorems on $ (CA)$ analytic groups, Trans. Amer. Math. Soc. 205 (1975), 181-192. MR 0364548 (51:802)
  • [7] -, Dense subgroups of Lie groups. II, Trans. Amer. Math. Soc. 246 (1978), 419-428. MR 515548 (80a:22009)

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Article copyright: © Copyright 1981 American Mathematical Society

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