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Journal of Lie Theory 16 (2006), No. 4, 601--620
Copyright Heldermann Verlag 2006

Effective Integration of Lie Algebras

Wojciech Wojtynski
Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland

For integrable Banach-Lie algebras the corresponding simply connected Banach-Lie groups are constructed in an explicite way. A concept of discriminant subgroup of a normed Lie algebra is introduced and it is shown that a Banach-Lie algebra is integrable if and only if its discriminant subgroup is discrete. Relation of discriminant subgroup with the Ado and Malcev theorems is also discussed.

Keywords: Banach-Lie algebra, integration of Lie algebras, B-C-H formula.

MSC: 22E65, 17B65

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