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arXiv · 1812.11883

Cayley-Klein Poisson homogeneous spaces

Francisco J. Herranz·Angel Ballesteros·Ivan Gutierrez-Sagredo·Mariano Santander
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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.

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Francisco J. Herranz, Angel Ballesteros, Ivan Gutierrez-Sagredo, Mariano Santander. 2018-12-31. Cayley-Klein Poisson homogeneous spaces. https://doi.org/10.7546/giq-20-2019-161-183

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