The relativistic noncommutative nonassociative group of velocities and the Thomas rotation

DOI10.1007/BF03322653zbMath0693.20067OpenAlexW1983801142MaRDI QIDQ584432

Abraham A. Ungar

Publication date: 1989

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03322653

zbMATH Keywords

special relativityThomas rotationLoopLorentz acceleration transformationsnoncommutative, nonassociative grouprelativistically admissible velocitiesweakly associativeweakly commutative

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Gravitational energy and conservation laws; groups of motions (83C40) Loops, quasigroups (20N05) General nonassociative rings (17A99) Multiply transitive infinite groups (20B22)

Related Items (13)

The equivalence of gyrocommutative gyrogroups and K-loops ⋮ Group-like structure underlying the unit ball in real inner product spaces ⋮ The Algebra of Gyrogroups: Cayley’s Theorem, Lagrange’s Theorem, and Isomorphism Theorems ⋮ Equivalence of two gyrogroup structures on unit balls ⋮ Middle Bruck loops and the total multiplication group ⋮ K-loops, gyrogroups and symmetric spaces ⋮ Extension of isometries in generalized gyrovector spaces of the positive cones ⋮ Weakly associative groups ⋮ The expanding Minkowski space ⋮ A characterization of Bol left loops. ⋮ The hyperbolic derivative in the Poincaré ball model of hyperbolic geometry ⋮ Hyperbolic trigonometry in the Einstein relativistic velocity model of hyperbolic geometry ⋮ Basarab loop and the generators of its total multiplication group

Cites Work

• The maximal sub near-field of a near-domain
• Special relativity with Clifford algebras and 2×2 matrices, and the exact product of two boosts
• ZT-subgroups of sharply 3-transitive groups

This page was built for publication: The relativistic noncommutative nonassociative group of velocities and the Thomas rotation