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Lie Group Structures on Quotient Groups and Universal Complexifications for Infinite-Dimensional Lie Groups

✍ Scribed by Helge Glöckner

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
541 KB
Volume
194
Category
Article
ISSN
0022-1236

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✦ Synopsis

We characterize the existence of Lie group structures on quotient groups and the existence of universal complexifications for the class of Baker-Campbell-Hausdorff (BCH-) Lie groups, which subsumes all Banach-Lie groups and ''linear'' direct limit Lie groups, as well as the mapping groups C r K ðM; GÞ :¼ fg 2 C r ðM; GÞ : gj M=K ¼ 1g; for every BCH-Lie group G; second countable finite-dimensional smooth manifold M; compact subset K of M; and 04r41: Also the corresponding test function groups D r ðM; GÞ ¼ S K C r K ðM; GÞ are BCH-Lie groups.

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