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Splittable Lie Groups and Lie Algebras

✍ Scribed by Michael Wüstner

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
118 KB
Volume
226
Category
Article
ISSN
0021-8693

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✦ Synopsis

We show that each Mal'cev splittable -Lie algebra (i.e., each -Lie algebra where ad is splittable) with char = 0 may be realized as a splittable subalgebra of a gl V , where V is a finite-dimensional vector space over , and that each Mal'cev splittable analytic subgroup of a GL n , i.e., each subgroup whose Lie algebra is Mal'cev splittable, can be realized as an analytic splittable subgroup of a GL m . Finally these results are applied to establish a necessary and sufficient condition for the exponential function of a Mal'cev splittable Lie group to be surjective.

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