Clifford Algebras and Possible Kinematics

Abstract

We review Bacry and Levy-Leblond's work on possible kinematics as applied to 2-dimensional spacetimes, as well as the nine types of 2-dimensional Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give homogeneous spacetimes for all but one of the kinematical groups. We then construct a two-parameter family of Clifford algebras that give a unified framework for representing both the Lie algebras as well as the kinematical groups, showing that these groups are true rotation groups. In addition we give conformal models for these spacetimes.

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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Cited by in corpus (6)

• Erlangen Program at Large-1: Geometry of Invariants
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications
• Group theoretical construction of planar Noncommutative Phase Spaces
• Clifford Fibrations and Possible Kinematics
• Cayley-Klein Poisson homogeneous spaces
• On exact representations of the motions group of Galilean plane