由对合环构造的代数群
Algebraic Groups Constructed From Rings with Involution
摘要：
我们定义了一类由具有对合的环构成的群。在适当的条件下，这些群是代数群或算术群，包括双曲4-空间的保向等距群，任意交换环$R$的$SL(2,R)$，各种辛群和正交群，以及$SO^+(4,1)$的一类重要的算术子群.我们调查时，这样的群体是同构和共轭的，并与此有关的问题，确定双曲$4$ -orbifolds同伦。
英文摘要：
We define a class of groups constructed from rings equipped with an involution. We show that under suitable conditions, these groups are either algebraic or arithmetic, including as special cases the orientation-preserving isometry group of hyperbolic 4-space, $SL(2,R)$ for any commutative ring $R$, various symplectic and orthogonal groups, and an important class of arithmetic subgroups of $SO^+(4,1)$. We investigate when such groups are isomorphic and conjugate, and relate this to problem of determining when hyperbolic $4$-orbifolds are homotopic.
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