Loop groups. (English) Zbl 0601.22011
Arbeitstag. Bonn 1984, Proc. Meet. Max-Planck-Inst. Math., Bonn 1984, Lect. Notes Math. 1111, 155-168 (1985).
[For the entire collection see Zbl 0547.00007.]
The loop group associated to a compact Lie group G is the group of smooth mappings of the circle \(S^ 1\) to G. The talk surveys what is known about the geometry and analysis connected with these groups. The existence of the one-parameter group of automorphisms of loop groups related to the rotations of the circle permits to speak about representations of positive energy. This is the main subject of the talk.
The loop group associated to a compact Lie group G is the group of smooth mappings of the circle \(S^ 1\) to G. The talk surveys what is known about the geometry and analysis connected with these groups. The existence of the one-parameter group of automorphisms of loop groups related to the rotations of the circle permits to speak about representations of positive energy. This is the main subject of the talk.
Reviewer: S.I.Gel’fand
MSC:
| 22E65 | Infinite-dimensional Lie groups and their Lie algebras: general properties |
| 22-02 | Research exposition (monographs, survey articles) pertaining to topological groups |
