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.
Repository Citation
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.
https://scholarworks.bgsu.edu/math_stat_pub/25
Publication Date
2014
Publication Title
Journal of Algebra
Publisher
Elsevier
DOI
https://doi.org/10.1016/j.jalgebra.2013.10.020
Volume
399
Issue
1
Start Page No.
978
End Page No.
1012