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A note on the Tits systems of Kac-Moody Steinberg groups. (English) Zbl 0910.22019
Let $$G$$ and $$H$$ denote the Chevalley (adjoint) and the Steinberg (nonadjoint) Kac-Moody group corresponding to a Kac-Moody algebra $$L$$, respectively. Let $$\sigma$$ denote the canonical homomorphism of $$H$$ onto $$G$$ which by an earlier result of the author is a canonical group map of the Weyl simple subgroup of $$H$$ onto $$G$$. In this note the author proves that the $$\sigma$$-inverse image of a Tits system in $$G$$ forms a Tits system in the Weyl simple subgroup of $$H$$.
##### MSC:
 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 20E42 Groups with a $$BN$$-pair; buildings
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