(2+1)维引力与Chern-Simons理论中的量子双和$\kappa$-庞加莱对称性
Quantum double and $κ$-Poincaré symmetries in (2+1)-gravity and Chern-Simons theory
AI总结：
该研究综述量子双和κ-庞加莱对称性在(2+1)维引力与陈-西蒙斯理论中的作用，明确二者的相容条件，指出类时形变κ-庞加莱对称性仅在德西特情形下关联陈-西蒙斯理论，且该理论与(2+1)维引力物理不等价。
摘要：
我们综述了Drinfeld doubles（德林费尔德双代数）和kappa-Poincare（κ-庞加莱）对称性在量子化(2+1)维引力与Chern-Simons（陈-西蒙斯）理论中的作用。我们讨论了给定Hopf代数（霍普夫代数）对称性与Chern-Simons理论相容的条件，并针对与(2+1)维引力等距群相关的Drinfeld doubles及kappa-Poincare对称性，明确确定了这种相容性。特别地，我们阐明了通常的类时形变kappa-Poincare对称性并不直接与(2+1)维引力相关。这类kappa-Poincare对称性仅在德西特情形下与Chern-Simons理论相关联，且对应的Chern-Simons理论在物理上与(2+1)维引力并不等价。
英文摘要：
We review the role of Drinfeld doubles and kappa-Poincare symmetries in quantised (2+1)-gravity and Chern-Simons theory. We discuss the conditions under which a given Hopf algebra symmetry is compatible with a Chern-Simons theory and determine this compatibility explicitly for the Drinfeld doubles and kappa-Poincare symmetries associated with the isometry groups of (2+1)-gravity. In particular, we explain that the usual kappa-Poincare symmetries with a timelike deformation are not directly associated with (2+1)-gravity. These kappa-Poincare symmetries are linked to Chern-Simons theory only in the de Sitter case, and the relevant Chern-Simons theory is physically inequivalent to (2+1)-gravity.
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