Defining relations of certain infinite dimensional groups. (English) Zbl 0625.22014

Élie Cartan et les mathématiques d’aujourd’hui, The mathematical heritage of Elie Cartan, Semin. Lyon 1984, Astérisque, No.Hors Sér. 1985, 165-208 (1985).
[For the entire collection see Zbl 0573.00010.]
The authors continue the study of the group G(A) associated to a Kac- Moody algebra and of “its unitary form” K(A). In contrast to their previous papers [Proc. Natl. Acad. Sci. USA 80, 1778-1782 (1983; Zbl 0512.17008), Prog. Math. 36, 141-166 (1983; Zbl 0578.17014) and Invent. Math. 76, 1-14 (1984; Zbl 0534.17008)] they define the groups G(A) and K(A) axiomatically and then give a detailed exposition of their structure. The notion of “refined Tits system” is introduced and then used to describe these groups. Presentation theorems for G(A) and K(A) are also proved.
Reviewer: A.Verona


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