English

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, SL(2,R)SL(2,R) for any commutative ring RR, various symplectic and orthogonal groups, and an important class of arithmetic subgroups of SO+(4,1)SO^+(4,1). We investigate when such groups are isomorphic and conjugate, and relate this to problem of determining when hyperbolic 44-orbifolds are homotopic.

Keywords

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