On Generalizations of Kac-Moody Groups
MFO Scientific ProgramResearch in Pairs 2009
Blok, Rieuwert J.
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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 twinbuildings. We mention that non-orientable Curtis-Tits groups exist. In the present paper we construct families of orientable and non-orientable Curtis-Tits groups. The resulting groups are quite interesting in their own right. The orientable ones are related to Drinfel’d’ 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 q-CCR algebras in physics and have symplectic, orthogonal and unitary groups as quotients.