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