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Generalized Hyperbolic Spaces Associated with Arbitrary Quadratic Forms

2021/12/31 by Shaul Zemel, Zemel, Shaul
Mathematics · Physics and Astronomy · #15A63 #15A66 #Algebraic and Geometric Analysis #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2201.00054

openalex publication_date 2021/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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