An infinite dimensional version of the third Lie theorem. (English) Zbl 1010.22025

Rybicki, Tomasz

Slovák, Jan (ed.) et al., The proceedings of the 21th winter school “Geometry and physics”, Srní, Czech Republic, January 13-20, 2001. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 69, 209-217 (2002).

The concept of evolution operator is used to introduce a weak Lie subgroup of a regular Lie group, and to give a new version of the third Lie theorem. This enables the author to formulate and to study the problem of integrability of infinite-dimensional Lie algebras. Several interesting examples are presented.
For the entire collection see [Zbl 0994.00029].

Reviewer: Constantin Udrişte (Bucureşti)

MSC:

22E65	Infinite-dimensional Lie groups and their Lie algebras: general properties
17B65	Infinite-dimensional Lie (super)algebras

Keywords:

weak Lie subgroup; regular Lie group; third Lie theorem; infinite-dimensional Lie algebras