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Remarks on the loop groups of compact Lie groups and the diffeomorphism group of the circle. (English. Russian original) Zbl 0968.22017

Proc. Steklov Inst. Math. 224, 124-136 (1999); translation from Tr. Mat. Inst. Steklova 224, 139-151 (1999).
The authors give some remarks on loop groups of compact Lie groups and the group of diffeomorphisms of the circle. It is shown that the properties of the loop groups are quite similar to the properties of finite dimensional (compact) Lie groups and are different from those of the group of diffeomorphisms of the circle.
For the entire collection see [Zbl 0942.00074].

MSC:

22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
22E67 Loop groups and related constructions, group-theoretic treatment
58D05 Groups of diffeomorphisms and homeomorphisms as manifolds
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