Groups associated with Kac-Moody algebras. (Groupes associés aux algèbres de Kac-Moody.) (French) Zbl 0705.17018

Sémin. Bourbaki, Vol. 31, 41e année (1988/1989), Exp. No. 700, Astérisque 177-178, 7-31 (1989).
This is an exposition on Kac-Moody groups. After giving an account of how various people (under various hypotheses) have constructed such groups the author explains in some details – but without proofs – how his own construction goes. For the proofs he refers to his paper [J. Algebra 105, 542–573 (1987; Zbl 0626.22013)]. The construction does not involve a choice of representation and in fact the author goes on to show how the usual simple highest weight modules for the underlying Kac-Moody algebra can be made into modules for his group. The paper also contains a section on Mathieu’s work on the so-called ind-group schemes and a final section with various comments and questions.
For the entire collection see [Zbl 0691.00001].
Reviewer: H. H. Andersen


17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
14L15 Group schemes


Zbl 0626.22013
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