Curtis–Tits groups generalizing Kac–Moody groups of type A˜n−1
Curtis–Tits groups generalizing Kac–Moody groups of type A˜n−1
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Curtis-Tits 群推广 A~n−1 类型的 Kac-Moody 群
DOI：
10.1016/j.jalgebra.2013.10.020
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发表时间：
2014
影响因子：
0.9
通讯作者：
Corneliu G. Hoffman
中科院分区：
文献类型：
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作者：
R. Blok;Corneliu G. Hoffman
在文[13]中，我们将Curtis-Tits群定义为Kac-Moody群的某种推广。我们区分了可定向Curtis-Tits群和不可定向Curtis-Tits群，并将所有可定向Curtis-Tits群确定为与孪生建筑相关的Kac-Moody群。在本文中，我们用图A˜n−1(n⩾4)在至少4个域k上构造了所有可定向和不可定向的Curtis-Tits群，得到的群本身很有趣。可定向的结果与DrinfeldʼS构造非交换射影直线上的向量丛有关，也与循环代数上的经典群有关。不可定向的与扩展图[14]有关，并且具有辛群、正交群和酉群作为商。
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.
Curtis-Tits 组的扩展图
DOI：
10.1016/j.jcta.2011.10.007
发表时间：
2012
期刊：
Journal of Combinatorial Theory, Series A
影响因子：
--
作者：
Blok R
通讯作者：
Blok R