Geometry of the Non-Compact G(2)

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.

arXiv comment7 pages, no figures

References in corpus (7)

• Quantum Field Theory on Noncommutative Spaces
• Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED
• Octonionic Electrodynamics
• Octonionic Geometry
• Geometrical Applications of Split Octonions
• Casimir operators of the exceptional group G2
• Octonionic geometry and conformal transformations

Cited by in corpus (3)

• Algebraical Entropy and Arrow of Time
• Dirac and Maxwell systems in split octonions
• Split octonionic Dirac equation