Generalized Hyperbolic Spaces Associated with Arbitrary Quadratic Forms
Group Theory
2022-01-04 v1
Abstract
The Vahlen group gives a way for presenting the hyperbolic space of every dimension of a group acting via M\"{o}bius transformations. As Vahlen groups and paravector Vahlen groups are now defined over any field of characteristic different from 2, we establish analogous spaces on which they operate transitively as M\"{o}bius transformations, by defining appropriate boundary components that must be added in case the denominator in the M\"{o}bius transformation formula vanishes.
Cite
@article{arxiv.2201.00054,
title = {Generalized Hyperbolic Spaces Associated with Arbitrary Quadratic Forms},
author = {Shaul Zemel},
journal= {arXiv preprint arXiv:2201.00054},
year = {2022}
}
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31 pages