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References (26)
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(i) g ¼ r ð g Þ l s ð g Þ is a direct sum algebraically and topologically of the radical and a unique Levi summand s ð g Þ -
i) The nilcore nilcore ð g Þ ¼ n ð g Þ = z ð g Þ of g is finite-dimensional -
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K. Hofmann, S. Morris (2007)
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If dim r ð g Þ 0 < y , then there is a finite-dimensional ideal f of g and a closed vector subspace a of z ð g Þ such that g is the ideal direct sum s ð g Þ l a l f , and g is very rich -
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ii) Its Lie algebra L ð nilcore ð G ÞÞ is naturally isomorphic to the nilcore nilcore ð g Þ of its Lie algebra g ¼ L ð G Þ -
Karl H. Hofmann, Fachbereich Mathematik, Darmstadt University of Technology, Schloss-gartenstr. 7, D-64289 Darmstadt, Germany hofmann@ -
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.10. Let g be a pro-Lie algebra satisfying n cored ð g Þ J z ð g Þ -
, all of the containments in the tall Hasse diagram are proper
- Publisher
- de Gruyter
- Copyright
- © Walter de Gruyter
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- DOI
- 10.1515/FORUM.2008.031
- Publisher site
- See Article on Publisher Site
Abstract
If the nilradical 𝔫(𝔤) of the Lie algebra 𝔤 of a pro-Lie group G is finite dimensional modulo the center 𝔷(𝔤), then every identity neighborhood U of G contains a closed normal subgroup N such that G/N is a Lie group and G and N × G/N are locally isomorphic. 2000 Mathematics Subject Classification: 22E65, 17B65, 22A05; 22E15, 22E60, 22E25, 22D05.
Journal
Forum Mathematicum – de Gruyter
Published: Jul 1, 2008