Subsemigroups of Semisimple Lie Groups

Abels H (2015)
Transformation Groups 20(2): 307-318.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Let G be a simple Lie group with finite center. We show that G can be algebraically generated as a semigroup by a one-parameter subsemigroup X (+) and one additional element g. In fact, given one of the two, a non-constant X (+) or a non-central g, there is a g, respectively X (+), such that the two together generate G as a semigroup. It follows that given a non-constant one-parameter subsemigroup X (+) of G there is another one-parameter subsemigroup Y (+) such that the two generate G as a semigroup. Similarly, given a non-central element g of G there is an element h of G such that the two generate a dense subsemigroup of G. We have analogous results for semismple Lie groups. For SL(2, a"e) and its universal cover we spell out when two one-parameter subsemigroups generate the group as a semigroup. On the way we prove results on open subsets of subsemigroups and on exponentiality, which may be of independent interest.
Erscheinungsjahr
2015
Zeitschriftentitel
Transformation Groups
Band
20
Ausgabe
2
Seite(n)
307-318
ISSN
1083-4362
Page URI
https://pub.uni-bielefeld.de/record/2758623

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Abels H. Subsemigroups of Semisimple Lie Groups. Transformation Groups. 2015;20(2):307-318.
Abels, H. (2015). Subsemigroups of Semisimple Lie Groups. Transformation Groups, 20(2), 307-318. doi:10.1007/s00031-015-9303-3
Abels, H. (2015). Subsemigroups of Semisimple Lie Groups. Transformation Groups 20, 307-318.
Abels, H., 2015. Subsemigroups of Semisimple Lie Groups. Transformation Groups, 20(2), p 307-318.
H. Abels, “Subsemigroups of Semisimple Lie Groups”, Transformation Groups, vol. 20, 2015, pp. 307-318.
Abels, H.: Subsemigroups of Semisimple Lie Groups. Transformation Groups. 20, 307-318 (2015).
Abels, Herbert. “Subsemigroups of Semisimple Lie Groups”. Transformation Groups 20.2 (2015): 307-318.