Weakly associative groups

DOI10.1007/BF03322638zbMath0699.20055MaRDI QIDQ912987

Abraham A. Ungar

Publication date: 1990

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

zbMATH Keywords

groupsspecial relativityThomas precessionLorentz grouprelativistically admissible velocitiesunique productsweakly associative groupoidweakly associative groupsweakly associative-commutative

Mathematics Subject Classification ID

Gravitational energy and conservation laws; groups of motions (83C40) Structure and representation of the Lorentz group (22E43) Loops, quasigroups (20N05) General nonassociative rings (17A99) Multiply transitive infinite groups (20B22)

Related Items (20)

Abstract space–times and their Lorentz groups ⋮ Gyrosemidirect product structure of bounded symmetric domains ⋮ Group-like structure underlying the unit ball in real inner product spaces ⋮ Equivalence of two gyrogroup structures on unit balls ⋮ Geometry of kinematic \(K\)-loops ⋮ The abstract complex Lorentz transformation group with real metric. II. The invariance group of the form ‖t‖2−∥x∥2 ⋮ The abstract complex Lorentz transformation group with real metric. I. Special relativity formalism to deal with the holomorphic automorphism group of the unit ball in any complex Hilbert space ⋮ K-loops, gyrogroups and symmetric spaces ⋮ \(K\)-loops from classical groups over ordered fields ⋮ The expanding Minkowski space ⋮ A characterization of Bol left loops. ⋮ Webs related to \(K\)-loops and reflection structures ⋮ \(K\)-loops and Bruck loops on \(\mathbb{R}\times\mathbb{R}\) ⋮ Examples of finite and infinite \(K\)-loops ⋮ A characterization of relativistic addition ⋮ Hyperbolic trigonometry in the Einstein relativistic velocity model of hyperbolic geometry ⋮ Comment on ``The expanding Minkowski space by A. A. Ungar ⋮ Loops and semidirect products ⋮ On \(K\)-loops of finite order ⋮ The holomorphic automorphism group of the complex disk

Cites Work

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• The relativistic noncommutative nonassociative group of velocities and the Thomas rotation
• The Thomas rotation formalism underlying a nonassociative group structure for relativistic velocities
• Theorie der verallgemeinerten kinematischen Räume. (Theory of generalized kinematic spaces)
• The maximal sub near-field of a near-domain
• Zusammenhänge zwischen Fastbereichen, scharf zweifach transitiven Permutationsgruppen und 2-Strukturen mit Rechtecksaxiom
• Bemerkungen über Fastbereiche und scharf zweifach transitive Gruppen. (Remarks on near-domains and sharply 2-transitive groups.)
• Conditions of finiteness on sharply 2-transitive groups
• Über eine scharf 3-fach transitiven Gruppen zugeordnete algebraische Struktur
• Special relativity with Clifford algebras and 2×2 matrices, and the exact product of two boosts
• ZT-subgroups of sharply 3-transitive groups

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