Cayley-Klein Poisson Homogeneous Spaces
作者: Francisco J. HerranzAngel BallesterosIvan Gutierrez-SagredoMariano Santander
论文集英文名称: Proceedings of the Twentieth International Conference on Geometry, Integrability and Quantization
来源数据库: Project Euclid
DOI: 10.7546/giq-20-2019-161-183
原始语种摘要: 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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  • Poisson 泊松
  • noncommutative 非交换的
  • Riemannian geometry[数]黎曼几何
  • homogeneous 均质的
  • curvature 曲率
  • quantization 量子化
  • corresponding 对应的
  • parameters 参数
  • constant 常数
  • lines 线型