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Journal of Lie Theory 15 (2005), No. 1, 335--339
Copyright Heldermann Verlag 2005

A Dynamical Approach to Compactify the Three Dimensional Lorentz Group

Marcos Salvai
FaMAF - CIEM, Ciudad Universitaria, 5000 Córdoba, Argentina

The Lorentz group acts on the projectivized light cone in the three dimensional Lorentz space as the group G of Möbius transformations of the circle. We find the closure of G in the space of all measurable functions of the circle into itself, obtaining a compactification of it as an open dense subset of the three-sphere, with a dynamical meaning related to generalized flows.

Keywords: Compactification, Lorentz group, Möbius transformation, generalized flow.

MSC: 53C22; 57S20, 58D15, 74A05

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