Uniqueness and presentation of Kac-Moody groups over fields
نویسندگان
چکیده
منابع مشابه
Kac-Moody groups over ultrametric fields
The Kac-Moody groups studied here are the minimal (=algebraic) and split ones, as introduced by J. Tits in [8]. When they are defined over an ultrametric field, it seems natural to associate to them some analogues of the Bruhat-Tits buildings. Actually I came to this problem when I was trying to build new buildings of nondiscrete type. If G is a Kac-Moody group over an ultrametric field K, I wa...
متن کاملUniqueness of Representation–theoretic Hyperbolic Kac–moody Groups over Z
For a simply laced and hyperbolic Kac–Moody group G = G(R) over a commutative ring R with 1, we consider a map from a finite presentation of G(R) obtained by Allcock and Carbone to a representation–theoretic construction G(R) corresponding to an integrable representation V λ with dominant integral weight λ. When R = Z, we prove that this map extends to a group homomorphism ρλ,Z : G(Z)→ G(Z). We...
متن کاملPresentation of Hyperbolic Kac–moody Groups over Rings
Tits has defined Kac–Moody and Steinberg groups over commutative rings, providing infinite dimensional analogues of the Chevalley–Demazure group schemes. Here we establish simple explicit presentations for all Steinberg and Kac–Moody groups whose Dynkin diagrams are hyperbolic and simply laced. Our presentations are analogues of the Curtis–Tits presentation of the finite groups of Lie type. Whe...
متن کاملExistence of Lattices in Kac Moody Groups over Finite Fields
Let g be a Kac–Moody Lie algebra. We give an interpretation of Tits’ associated group functor using representation theory of g and we construct a locally compact “Kac–Moody group” G over a finite field k. Using (twin) BN-pairs (G,B,N) and (G,B−, N) for G we show that if k is “sufficiently large”, then the subgroup B− is a non-uniform lattice in G. We have also constructed an uncountably infinit...
متن کاملPresentation of Affine Kac-moody Groups over Rings
Tits has defined Steinberg groups and Kac-Moody groups for any root system and any commutative ring R. We establish a Curtis-Tits-style presentation for the Steinberg group St of any rank ≥ 3 irreducible affine root system, for any R. Namely, St is the direct limit of the Steinberg groups coming from the 1and 2-node subdiagrams of the Dynkin diagram. This leads to a completely explicit presenta...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1987
ISSN: 0021-8693
DOI: 10.1016/0021-8693(87)90214-6