The Einstein relativistic velocity model of hyperbolic geometry and its plane separation axiom

DOI10.1007/s00006-012-0367-zzbMath1266.51026OpenAlexW1990826912WikidataQ114018390 ScholiaQ114018390MaRDI QIDQ1945474

Nilgün Sönmez, Abraham A. Ungar

Publication date: 8 April 2013

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00006-012-0367-z

zbMATH Keywords

Möbius additionhyperbolic geometrygyrogroupEinstein velocity additiongyrovector spaceplane separation axiom

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Special relativity (83A05) Euclidean geometries (general) and generalizations (51M05)

Related Items (4)

The Algebra of Gyrogroups: Cayley’s Theorem, Lagrange’s Theorem, and Isomorphism Theorems ⋮ Novel Tools to Determine Hyperbolic Triangle Centers ⋮ The quartet of eigenvectors for quaternionic Lorentz transformation ⋮ Einstein gyrogroup as a B-loop

Cites Work

• Möbius gyrogroups: a Clifford algebra approach.
• When relativistic mass meets hyperbolic geometry
• Factorizations of Möbius gyrogroups.
• Spherical continuous wavelet transforms arising from sections of the Lorentz group
• Geometry of homogeneous Lie loops
• Lie gyrovector spaces
• Strong near subgroups and left gyrogroups
• Gyrogroups and homogeneous loops
• Hyperbolic triangle centers. The special relativistic approach
• Old and new in Möbius groups
• From Möbius to Gyrogroups
• A Gyrovector Space Approach to Hyperbolic Geometry
• Spaces of Holomorphic Functions in the Unit Ball
• Involutory decomposition of groups into twisted subgroups and subgroups
• Gyrogroups and the decomposition of groups into twisted subgroups and subgroups.
• Beyond the Einstein addition law and its gyroscopic Thomas precession. The theory of gyrogroups and gyrovector spaces
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