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

Wojciech Wojtyński

Studia Mathematica (1994)

  • Volume: 111, Issue: 2, page 163-185
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Wojtyński, Wojciech. "One-parameter subgroups and the B-C-H formula." Studia Mathematica 111.2 (1994): 163-185. <http://eudml.org/doc/216126>.

@article{Wojtyński1994,
abstract = {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.},
author = {Wojtyński, Wojciech},
journal = {Studia Mathematica},
keywords = {Lie theory; topological groups; one-parameter subgroups; Baker-Campbell-Hausdorff formula; Lie algebra},
language = {eng},
number = {2},
pages = {163-185},
title = {One-parameter subgroups and the B-C-H formula},
url = {http://eudml.org/doc/216126},
volume = {111},
year = {1994},
}

TY - JOUR
AU - Wojtyński, Wojciech
TI - One-parameter subgroups and the B-C-H formula
JO - Studia Mathematica
PY - 1994
VL - 111
IS - 2
SP - 163
EP - 185
AB - 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.
LA - eng
KW - Lie theory; topological groups; one-parameter subgroups; Baker-Campbell-Hausdorff formula; Lie algebra
UR - http://eudml.org/doc/216126
ER -

References

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  9. [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. [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. [11] J. Palis, Vector fields generate few diffeomorphisms, Bull. Amer. Math. Soc. 80 (1974), 503-505. Zbl0296.57008
  12. [12] J.-P. Serre, Lie Algebras and Lie Groups, Benjamin, New York, 1965. 
  13. [13] S.-S. Chen and R. Yoh, The category of generalized Lie groups, Trans. Amer. Math. Soc. 199 (1974), 281-294. Zbl0291.22003
  14. [14] W. Thurston, Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc. 80 (1974), 304-307. Zbl0295.57014

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