Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cayley-Klein Poisson homogeneous spaces   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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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th