Curtis-Tits groups generalizing Kac-Moody groups of type A~n-1

Abstract

In [13] 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 Drinfeld's 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 [14] and have symplectic, orthogonal and unitary groups as quotients. © 2013 .