Generalized Hyperbolic Spaces Associated with Arbitrary Quadratic Forms
Abstract
The Vahlen group gives a way for presenting the hyperbolic space of every dimension of a group acting via M\"obius 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\"obius transformations, by defining appropriate boundary components that must be added in case the denominator in the M\"obius transformation formula vanishes.
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