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arXiv · 2005.00679

Algebraic Groups Constructed From Rings with Involution

Arseniy Sheydvasser
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Abstract

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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Arseniy Sheydvasser. 2020-05-02. Algebraic Groups Constructed From Rings with Involution. https://arxiv.org/abs/2005.00679

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