论文标题
由环构建的代数群
Algebraic Groups Constructed From Rings with Involution
论文作者
论文摘要
我们定义了一类由配备有涉及的环构建的组。我们表明，在适当的条件下，这些组是代数或算术，包括特殊情况下的蜂鸣器4空间的定向式等轴测组，$ sl（2，r）$，用于任何交换ring $ r $，各种符号和正交组和正交组，以及重要的Arithmetic子组，以及$ so so^+（4,4,1）$（4,1,1）$。我们调查了此类组何时是同构和共轭物，并将其与确定何时双曲线$ 4 $ -Orbifolds的问题联系起来。
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.
