Effective integration of Lie algebras

摘要

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.