Five new families of noncommutative lightcones in dimensions are presented as quantizations of the inequivalent Poisson homogeneous structures that emerge when the lightcone is constructed as a homogeneous space of the SO(2,1) conformal group. Each of these noncommutative lightcones maintains covariance under the action of the respective quantum deformation of the SO(2,1) conformal group. We discuss the role played by SO(2,1) automorphisms in the classification of inequivalent Poisson homogeneous lightcones, as well as the geometric aspects of this construction. The localization properties of the novel quantum lightcones are analyzed and shown to be deeply connected with the geometric features of the Poisson homogeneous spaces.

中文翻译：

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来自量子 SO（2,1） 保形群的非交换光锥


五个新的维度非交换光锥族表示为当光锥构建为 SO（2,1） 保形群的均质空间时出现的不等价泊松齐次结构的量子化。这些非交换光锥中的每一个在 SO（2,1） 保形群的相应量子变形的作用下保持协方差。我们讨论了 SO（2,1） 自同态在不等价泊松齐次光锥分类中的作用，以及这种结构的几何方面。分析了新型量子光锥的定位特性，并表明它与泊松齐次空间的几何特征密切相关。