Uniqueness of Representation–theoretic Hyperbolic Kac–moody Groups over Z
نویسندگان
چکیده
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 prove that the kernel K of ρλ,Z lies in H(C) and if the natural group homomorphism φ : G(Z)→ G(C) is injective, then K ≤ H(Z) ∼= (Z/2Z).
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