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1994 | 111 | 2 | 163-185
Tytuł artykułu

One-parameter subgroups and the B-C-H formula

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EN
Abstrakty
EN
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
111
Numer
2
Strony
163-185
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-04-04
poprawiono
1993-12-14
Twórcy
  • Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
  • [1] G. Birkhoff, Analytical groups, Trans. Amer. Math. Soc. 43 (1938), 61-101.
  • [2] N. Bourbaki, Groupes et algèbres de Lie, Chap. II, Hermann, Paris, 1971.
  • [3] D. B. A. Epstein, The simplicity of certain groups of homeomorphisms, Compositio Math. 22 (1970), 165-173.
  • [4] J. Grabowski and W. Wojtyński, Quotient groups of linear topological spaces, Colloq. Math. 59 (1991), 35-51.
  • [5] M. Herman, Simplicité du groupe des difféomorphismes de classe $C^∞$, isotopes à l'identité, du tore de dimension n, C. R. Acad. Sci. Paris Sér. A 273 (1971), 232-234.
  • [6] J. Leslie, On a differentiable structure for the group of diffeomorphisms, Topology 6 (1967), 263-271.
  • [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).
  • [8] B. Maissen, Lie-Gruppen mit Banachräumen als Parameterräumen, Acta Math. 108 (1962), 229-269.
  • [9] J. Milnor, Remarks on infinite-dimensional Lie groups, in: Relativity, Groups and Topology, II (Les Houches, 1983), North-Holland, Amsterdam, 1984, 1007-1057.
  • [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.
  • [11] J. Palis, Vector fields generate few diffeomorphisms, Bull. Amer. Math. Soc. 80 (1974), 503-505.
  • [12] J.-P. Serre, Lie Algebras and Lie Groups, Benjamin, New York, 1965.
  • [13] S.-S. Chen and R. Yoh, The category of generalized Lie groups, Trans. Amer. Math. Soc. 199 (1974), 281-294.
  • [14] W. Thurston, Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc. 80 (1974), 304-307.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv111i2p163bwm
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