An algebraic scheme for Lie theory of topological groups with "large" families of one-parameter subgroups is proposed. Such groups are quotients of "𝔼ℝ-groups", i.e. topological groups equipped additionally with the continuous exterior binary operation of multiplication by real numbers, and generated by special ("exponential") elements. It is proved that under natural conditions on the topology of an 𝔼ℝ-group its group multiplication is described by the B-C-H formula in terms of the associated Lie algebra.
@article{bwmeta1.element.bwnjournal-article-smv111i2p163bwm,
author = {Wojciech Wojty\'nski},
title = {One-parameter subgroups and the B-C-H formula},
journal = {Studia Mathematica},
volume = {108},
year = {1994},
pages = {163-185},
zbl = {0838.22007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv111i2p163bwm}
}
Wojtyński, Wojciech. One-parameter subgroups and the B-C-H formula. Studia Mathematica, Tome 108 (1994) pp. 163-185. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv111i2p163bwm/
[00000] [1] G. Birkhoff, Analytical groups, Trans. Amer. Math. Soc. 43 (1938), 61-101. | Zbl 0018.20502
[00001] [2] N. Bourbaki, Groupes et algèbres de Lie, Chap. II, Hermann, Paris, 1971.
[00002] [3] D. B. A. Epstein, The simplicity of certain groups of homeomorphisms, Compositio Math. 22 (1970), 165-173. | Zbl 0205.28201
[00003] [4] J. Grabowski and W. Wojtyński, Quotient groups of linear topological spaces, Colloq. Math. 59 (1991), 35-51. | Zbl 0727.22005
[00004] [5] M. Herman, Simplicité du groupe des difféomorphismes de classe , isotopes à l’identité, du tore de dimension n, C. R. Acad. Sci. Paris Sér. A 273 (1971), 232-234. | Zbl 0217.49602
[00005] [6] J. Leslie, On a differentiable structure for the group of diffeomorphisms, Topology 6 (1967), 263-271. | Zbl 0147.23601
[00006] [7] Yu. V. Linnik, An elementary solution of the problem of Waring by the Schnirelmann method, Mat. Sb. (N.S.) 12 (1943), 225-230 (in Russian).
[00007] [8] B. Maissen, Lie-Gruppen mit Banachräumen als Parameterräumen, Acta Math. 108 (1962), 229-269.
[00008] [9] J. Milnor, Remarks on infinite-dimensional Lie groups, in: Relativity, Groups and Topology, II (Les Houches, 1983), North-Holland, Amsterdam, 1984, 1007-1057.
[00009] [10] H. Omori, On the group of diffeomorphisms of a compact manifold, in: Global Analysis, Proc. Sympos. Pure Math. 15, Amer. Math. Soc., 1970, 167-183.
[00010] [11] J. Palis, Vector fields generate few diffeomorphisms, Bull. Amer. Math. Soc. 80 (1974), 503-505. | Zbl 0296.57008
[00011] [12] J.-P. Serre, Lie Algebras and Lie Groups, Benjamin, New York, 1965.
[00012] [13] S.-S. Chen and R. Yoh, The category of generalized Lie groups, Trans. Amer. Math. Soc. 199 (1974), 281-294. | Zbl 0291.22003
[00013] [14] W. Thurston, Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc. 80 (1974), 304-307. | Zbl 0295.57014