Geometry of the Non-Compact G(2)

Merab Gogberashvili; Alexandre Gurchumelia

doi:10.1016/j.geomphys.2019.06.015

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arXiv · 1903.04888

Geometry of the Non-Compact G(2)

Merab Gogberashvili·Alexandre Gurchumelia

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Abstract

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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Merab Gogberashvili, Alexandre Gurchumelia. 2019-03-08. Geometry of the Non-Compact G(2). https://doi.org/10.1016/j.geomphys.2019.06.015

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