(CA) closures of analytic groups

Author:
David Zerling

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

MSC:
Primary 22E05

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

MathSciNet review:
603616

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An analytic group is called if the group of inner automorphisms of is closed in the Lie group of all bicontinuous automorphisms of . We introduce the notion of a closure for an analytic group and show that every analytic group possesses a closure. The definition of uniqueness for such a 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 analytic group to be .

**[1]**M. Goto,*Analytic subgroups of*, 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**Lie algebras*. I, II, Indag. Math.**14**(1952), 546-568.**[6]**D. Zerling,*Some theorems on**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)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
22E05

Retrieve articles in all journals with MSC: 22E05

Additional Information

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

Article copyright:
© Copyright 1981
American Mathematical Society