Octonionic Mobius Transformations

Abstract

A vexing problem involving nonassociativity is resolved, allowing a generalization of the usual complex Mobius transformations to the octonions. This is accomplished by relating the octonionic Mobius transformations to the Lorentz group in 10 spacetime dimensions. The result will be of particular interest to physicists working with lightlike objects in 10 dimensions.

Plain TeX, 12 pages, 1 PostScript figure included using epsf

References in corpus (1)

• Finite Lorentz Transformations, Automorphisms, and Division Algebras

Cited by in corpus (7)

• Black Holes, Qubits and Octonions
• Hyperbolic Weyl groups and the four normed division algebras
• Generalized non-associative structures on the 7-sphere
• Geometry of Riccati equations over normed division algebras
• Division Algebra Representations of SO(4,2)
• Octonionic presentation for the Lie group $SL(2,\mathbb{O})$
• Yang-Mills connections valued on the octonionic algebra