Curtis–Tits Groups Generalizing Kac–Moody Groups of Type An−1
In  we define a Curtis–Tits group as a certain generalization of a Kac–Moody group. We distinguish between orientable and non-orientable Curtis–Tits groups and identify all orientable Curtis–Tits groups as Kac–Moody groups associated to twin-buildings. In the present paper we construct all orientable as well as non-orientable Curtis–Tits groups with diagram A˜n−1 (n⩾4) over a field k of size at least 4. The resulting groups are quite interesting in their own right. The orientable ones are related to Drinfeldʼs construction of vector bundles over a non-commutative projective line and to the classical groups over cyclic algebras. The non-orientable ones are related to expander graphs  and have symplectic, orthogonal and unitary groups as quotients.
Blok, Rieuwert J. and Hoffman, Corneliu G., "Curtis–Tits Groups Generalizing Kac–Moody Groups of Type An−1" (2014). Mathematics and Statistics Faculty Publications. 25.
Journal of Algebra
Start Page No.
End Page No.