Extension of the unit disk gyrogroup into the unit ball of any real inner product space

DOI10.1006/JMAA.1996.0359zbMath0865.20055OpenAlexW1988507221MaRDI QIDQ1923923

Abraham A. Ungar

Publication date: 14 July 1997

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1996.0359

zbMATH Keywords

Möbius transformationshyperbolic spacesBruck loopsgyrogroupsmotion groupsreal inner product spaces\(k\)-loopsgeneralized Poincaré metricopen balls

Mathematics Subject Classification ID

Special relativity (83A05) Structure and representation of the Lorentz group (22E43) Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Loops, quasigroups (20N05) Extensions, wreath products, and other compositions of groups (20E22) Monogenic and polygenic functions of one complex variable (30A05)

Related Items (15)

A Cauchy type inequality for Möbius operations ⋮ On a notion of complex Möbius gyrovector spaces ⋮ Equivalence of two gyrogroup structures on unit balls ⋮ Orthogonal gyroexpansion in Möbius gyrovector spaces ⋮ Unnamed Item ⋮ Seeing the Möbius disc-transformation group like never before. ⋮ A Cauchy-Bunyakovsky-Schwarz type inequality related to the Möbius addition ⋮ The hyperbolic derivative in the Poincaré ball model of hyperbolic geometry ⋮ Möbius gyrogroups: a Clifford algebra approach. ⋮ Cauchy-Bunyakovsky-Schwarz type inequalities related to Möbius operations ⋮ On Lipschitz continuity with respect to the Poincaré metric of linear contractions between Möbius gyrovector spaces ⋮ Continuous quasi gyrolinear functionals on Möbius gyrovector spaces ⋮ A geometric interpretation of Ungar's addition and of gyration in the hyperbolic plane ⋮ Hyperbolic trigonometry in the Einstein relativistic velocity model of hyperbolic geometry ⋮ Harmonic analysis on the Möbius gyrogroup

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