通过Drinfel'd实现（3+1）引力与宇宙学常数翻倍
Towards (3+1) gravity through Drinfel'd doubles with cosmological constant
摘要：
本文将（2+1）（Anti）-de Sitter和Poincaré李代数的量子变形推广到（3+1）维，它与（2+1）引力的Chern-Simons公式所施加的条件相容.由于这种相容性是由来自Drinfel'd双结构的变形自动实现的，我们相信，在（3+1）方案中，作为描述（3+1）引力的可能指导原则，也值得分析所述结构。为此，我们得到了三个（3+1）Lorentz代数的一个由Drinfel'd二重结构产生的典型的经典$r$ -矩阵.这个$r$ -矩阵是对应于（3+1）$κ$ -变形的矩阵的扭曲形式，并分析了与之相关的非对易时空的主要性质.特别地，证明了这种新的量子时空与$κ$ -Minkowski时空不同构，并且通过适当地改变量子代数生成元的基，量子空间坐标的各向同性可以保持.在整篇论文中，宇宙学常数作为一个明确的参数出现，因此可以直接得到庞加莱极限。
英文摘要：
We present the generalisation to (3+1) dimensions of a quantum deformation of the (2+1) (Anti)-de Sitter and Poincaré Lie algebras that is compatible with the conditions imposed by the Chern-Simons formulation of (2+1) gravity. Since such compatibility is automatically fulfilled by deformations coming from Drinfel'd double structures, we believe said structures are worth being analysed also in the (3+1) scenario as a possible guiding principle towards the description of (3+1) gravity. To this aim, a canonical classical $r$-matrix arising from a Drinfel'd double structure for the three (3+1) Lorentzian algebras is obtained. This $r$-matrix turns out to be a twisted version of the one corresponding to the (3+1) $κ$-deformation, and the main properties of its associated noncommutative spacetime are analysed. In particular, it is shown that this new quantum spacetime is not isomorphic to the $κ$-Minkowski one, and that the isotropy of the quantum space coordinates can be preserved through a suitable change of basis of the quantum algebra generators. Throughout the paper the cosmological constant appears as an explicit parameter, thus allowing the (flat) Poincaré limit to be straightforwardly obtained.
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