Algebraic Groups Constructed From Rings with Involution
Number Theory
2020-05-05 v1
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, for any commutative ring , various symplectic and orthogonal groups, and an important class of arithmetic subgroups of . We investigate when such groups are isomorphic and conjugate, and relate this to problem of determining when hyperbolic -orbifolds are homotopic.
Cite
@article{arxiv.2005.00679,
title = {Algebraic Groups Constructed From Rings with Involution},
author = {Arseniy Sheydvasser},
journal= {arXiv preprint arXiv:2005.00679},
year = {2020}
}
Comments
This is essentially a re-draft of arXiv:1908.01250. However, as there have been significant changes (including the title), it made sense to resubmit as a separate document