Smooth Loops and Thomas Precession

Alexander I. Nesterov; Lev V. Sabinin

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arXiv · 1304.7763

Smooth Loops and Thomas Precession

Alexander I. Nesterov·Lev V. Sabinin

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Abstract

Fundamentals of the local smooth loops due to Sabinin are concisely outlined together with the corresponding infinitesimal objects, so-called \nu-hyperalgebras, and the analogue of the Lie groups theory. We apply here this theory to to formulation of a new concept of loop of boosts. A quaternionic model of the three-parametric loop of boosts is obtained and a remarkable connection with geodesic loops of Lobachevskii space is found. A description of Thomas precession in the light of general theory of smooth loops is given.

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Alexander I. Nesterov, Lev V. Sabinin. 2013-04-27. Smooth Loops and Thomas Precession. https://arxiv.org/abs/1304.7763

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