Orders in Quaternion Algebras
Orders in Quaternion Algebras
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四元数代数中的阶
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
A. Reid
中科院分区：
文献类型：
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作者：
C. Maclachlan;A. Reid
第二章给出了四元数代数的基本代数理论。这足以满足迄今为止从克莱因群的不变迹域kΓ和不变四元数代数AΓ推导出关于它的信息所得到的结果。关于数域上四元数代数的算术理论，我们还没有详细的论述。这将是必不可少的，在提取更多的信息，四元数代数，更重要的是，在推导存在的离散Kleinian群的有限covolume。这些将是算术Kleinian群，本书其余部分将大量关注这些群。所有这些都是基于四元数代数的序结构，它封装了四元数代数的算术理论。这些在第2章中已经介绍过，但我们现在要做一个更系统的研究，特别是从局部-全局的角度。
The basic algebraic theory of quaternion algebras was given in Chapter 2. That sufficed for the results obtained so far on deducing information on a Kleinian group Γ from its invariant trace field kΓ and invariant quaternion algebra AΓ. We have yet to expound on the arithmetic theory of quaternion algebras over number fields. This will be essential in extracting more information on the quaternion algebras and, more importantly, in deducing the existence of discrete Kleinian groups of finite covolume. These will be arithmetic Kleinian groups about which a great deal of the remainder of the book will be concerned. All of this is based around the structure of orders in quaternion algebras which encapsulate the arithmetic theory of quaternion algebras. These were introduced in Chapter 2, but we now give a more systematic study, particularly from a local-global viewpoint.