对合域嵌入到对合单代数中的局部-整体原理
Local-global principles for embedding of fields with involution into simple algebras with involution
摘要：
本文证明了具有对合的域嵌入整体域上具有对合的中心单代数的局部-整体原理。这对研究整体域上的典型群是有意义的。本文证明了在D_n，n>4的偶数群中，两个弱可分解的Zagliki稠密S-等差子群实际上是可分解的.这个结果的一个推论是：给定D_n型的绝对单代数K-群G，n>4偶数，K是数域，G的任意K-形式G'具有与G相同的极大K-环面的同构类集，必与G K-同构。这些结果导出了n为偶数的2n-1维等长和等谱紧致双曲空间的结果。
英文摘要：
In this paper we prove local-global principles for embedding of fields with involution into central simple algebras with involution over a global field. These should be of interest in study of classical groups over global fields. We deduce from our results that in a group of type D_n, n>4 even, two weakly commensurable Zariski-dense S-arithmetic subgroups are actually commensurable. A consequence of this result is that given an absolutely simple algebraic K-group G of type D_n, n>4 even, K a number field, any K-form G' of G having the same set of isomorphism classes of maximal K-tori as G, is necessarily K-isomorphic to G. These results lead to results about isolength and isospectral compact hyperbolic spaces of dimension 2n-1 with n even.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
