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Geometry of the Non-Compact G(2)

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arxiv 1903.04888 v1 pith:42HPG2QI submitted 2019-03-08 physics.gen-ph

Merab Gogberashvili , Alexandre Gurchumelia This is my paper · ORCID
classification physics.gen-ph
keywords non-compactcasimircoordinatesextragrouppoincarerotationstime-like
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Geometrical applications of the non-compact form of Cartan's exceptional Lie group G(2) is considered. This group generates specific rotations of 7-dimensional Minkowski-like space with three extra time-like coordinates and in some limiting cases imitates standard Poincare transformations. In this model space-time translations are non-commutative and are represented by the rotations towards the extra time-like coordinates. The second order Casimir element of non-compact G(2) and its expression by the Casimir operators of the Lorentz and Poincare groups are found.

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Cited by 1 Pith paper

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  1. The Dirac equation in (split-)octonions: origins, variants, and modern context

    math-ph 2026-06 conditional novelty 5.0 of 10

    Four approaches to the Dirac equation in (split-)octonions are classified; a 2024 split-octonionic equation is shown identical to the 2006 2-factor form by structure-preserving rotation and relabeling.

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