### Abstract

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 PSL_{2}(ℝ). Using the methods developed in [3] 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) |
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Pages (from-to) | 361-370 |

Number of pages | 10 |

Journal | Publicationes Mathematicae |

Volume | 70 |

Issue number | 3-4 |

State | Published - Jun 12 2007 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Nagy, P. T., & Stuhl, I. (2007). Differentiable loops on the real line.

*Publicationes Mathematicae*,*70*(3-4), 361-370.