Abstract space–times and their Lorentz groups

DOI10.1063/1.531555zbMath0863.20035OpenAlexW2050438726MaRDI QIDQ5284263

Abraham A. Ungar, Jonathan D. H. Smith

Publication date: 26 May 1997

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531555

zbMATH Keywords

Lorentz groupsgyrogroupsrelativistically admissible velocitiesEuclidean three-space

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Applications of global differential geometry to the sciences (53C80) Special relativity (83A05) Structure and representation of the Lorentz group (22E43) Loops, quasigroups (20N05) Classical or axiomatic geometry and physics (51P05)

Related Items (6)

The Algebra of Gyrogroups: Cayley’s Theorem, Lagrange’s Theorem, and Isomorphism Theorems ⋮ Equivalence of two gyrogroup structures on unit balls ⋮ Complex boosts: a Hermitian Clifford algebra approach ⋮ Seeing the Möbius disc-transformation group like never before. ⋮ Einstein's velocity addition law and its hyperbolic geometry ⋮ Hyperbolic trigonometry in the Einstein relativistic velocity model of hyperbolic geometry

Cites Work

• Examples of finite and infinite \(K\)-loops
• Comment on ``The expanding Minkowski space by A. A. Ungar
• Weakly associative groups
• The expanding Minkowski space
• On generalized cocycle equations
• The holomorphic automorphism group of the complex disk
• Equivalence of two gyrogroup structures on unit balls
• Zusammenhänge zwischen Fastbereichen, scharf zweifach transitiven Permutationsgruppen und 2-Strukturen mit Rechtecksaxiom
• The abstract Lorentz transformation group
• The abstract complex Lorentz transformation group with real metric. II. The invariance group of the form ‖t‖2−∥x∥2

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