کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6414768 | 1630515 | 2014 | 35 صفحه PDF | دانلود رایگان |
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 AËnâ1 (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.
Journal: Journal of Algebra - Volume 399, 1 February 2014, Pages 978-1012