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VOL. 20 | 2019 Cayley-Klein Poisson Homogeneous Spaces
Francisco J. Herranz, Angel Ballesteros, Ivan Gutierrez-Sagredo, Mariano Santander

Editor(s) Ivaïlo M. Mladenov, Vladimir Pulov, Akira Yoshioka

Abstract

The nine two-dimensional Cayley-Klein geometries are firstly reviewed by following a graded contraction approach. Each geometry is considered as a set of three symmetrical homogeneous spaces (of points and two kinds of lines), in such a manner that the graded contraction parameters determine their curvature and signature. Secondly, new Poisson homogeneous spaces are constructed by making use of certain Poisson-Lie structures on the corresponding motion groups. Therefore, the quantization of these spaces provides noncommutative analogues of the Cayley-Klein geometries. The kinematical interpretation for the semi-Riemannian and pseudo-Riemannian Cayley-Klein geometries is emphasized, since they are just Newtonian and Lorentzian spacetimes of constant curvature.

Information

Published: 1 January 2019
First available in Project Euclid: 21 December 2018

zbMATH: 07060437
MathSciNet: MR3887749

Digital Object Identifier: 10.7546/giq-20-2019-161-183

Rights: Copyright © 2019 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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