Mathematics and Statistics Faculty Publications

Title

Curtis–Tits Groups Generalizing Kac–Moody Groups of Type An−1

Document Type

Article

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 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 [14] and have symplectic, orthogonal and unitary groups as quotients.

Publication Date

2014

Publication Title

Journal of Algebra

Volume

399

Start Page No.

978

End Page No.

1012

ISSN

0021-8693

DOI

10.1016/j.jalgebra.2013.10.020

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