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On the Surjectivity of the Exponential Function of Solvable Lie Groups

✍ Scribed by Michael Wüstner

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
663 KB
Volume
192
Category
Article
ISSN
0025-584X

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✦ Synopsis

For a solvable Lie group G the surjectivity of the exponential function expc is equivalent to the connectedness of the near-Cartan subgroups and to the connectedness of the centralizers in a Cartan subgroup of all nilpotent elements in its Lie algebra g. Furthermore, these conditions are satisfied if and only if for all elements g E G there is an x E g with g = expc x in which expC is regular. SL(2, a). A Lie group G is called exponential if its exponential function is surjective.

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