Fundamentals of the theory of Lie groups. (Russian) Zbl 0656.22002

Vinberg, Eh. B.; Onishchik, A. L.

Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 20, 5-101 (1988).

The basic notions and results of the theory of Lie groups are exposed including the correspondence between Lie groups and Lie algebras, universal enveloping algebras of Lie algebras and their applications. By way of a survey, some generalizations of this theory are considered: Lie groups over completely normed fields, infinite-dimensional Lie groups, analytic loops.

MSC:

22Exx	Lie groups
22E65	Infinite-dimensional Lie groups and their Lie algebras: general properties
17B35	Universal enveloping (super)algebras
22-02	Research exposition (monographs, survey articles) pertaining to topological groups
17B67	Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
17B45	Lie algebras of linear algebraic groups

Keywords:

Lie groups; Lie algebras; universal enveloping algebras; infinite- dimensional Lie groups; analytic loops