Octonionic Mobius Transformations
Corinne A. Manogue, Tevian Dray
TL;DR
This paper generalizes Mobius transformations to octonions by linking them to the Lorentz group in 10D, addressing nonassociativity issues and providing new tools for theoretical physics involving lightlike objects.
Contribution
It introduces a novel framework for octonionic Mobius transformations by connecting them to the 10D Lorentz group, overcoming nonassociativity challenges.
Findings
Established a relation between octonionic transformations and 10D Lorentz group
Resolved nonassociativity issues in octonionic transformations
Potential applications in physics involving 10-dimensional spacetime
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.
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