From Möbius to Gyrogroups

DOI10.1080/00029890.2008.11920506zbMath1152.30045arXiv1302.2122OpenAlexW1833616859WikidataQ58279457 ScholiaQ58279457MaRDI QIDQ3505013

Abraham A. Ungar

Publication date: 18 June 2008

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.2122

zbMATH Keywords

gyrogroupsMoebius groups

Mathematics Subject Classification ID

Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (15)

Möbius's functional equation and Schur's lemma with applications to the complex unit disk ⋮ Geometry of gyrogroups via Klein's approach ⋮ Unnamed Item ⋮ The Algebra of Gyrogroups: Cayley’s Theorem, Lagrange’s Theorem, and Isomorphism Theorems ⋮ A characterization of Möbius transformations by use of hyperbolic regular polygons ⋮ Einstein gyrogroup as a B-loop ⋮ The Einstein relativistic velocity model of hyperbolic geometry and its plane separation axiom ⋮ On Metric Structures of Normed Gyrogroups ⋮ An Inequality Related to Möbius Transformations ⋮ Möbius gyrogroups: a Clifford algebra approach. ⋮ A new proof of the nonexistence of isometries between higher dimensional Euclidean and hyperbolic spaces ⋮ Embedding of locally compact Hausdorff topological gyrogroups in topological groups ⋮ Extension of Maschke’s theorem ⋮ Harmonic analysis on the Möbius gyrogroup ⋮ Gyrogroup actions: a generalization of group actions

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