The paper is devoted to the study of differentiable loops L on the real line such that the group G topologically generated by the left translations is locally compact and hence it is isomorphic to the universal covering group of PSL2(ℝ). Using the methods developed in  we introduce a class of natural parametrizations of the loop manifold L corresponding to the Iwasava decompositions of G and find explicit expressions for the loop multiplication with respect to the given parametrizations. We characterize the differentiable curves ℝ → G consisting of the left translations of a loop L in the biinvariant Lorentzian geometry of G.
|Original language||English (US)|
|Number of pages||10|
|State||Published - Jun 12 2007|
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