Abstract We derive the non-relativistic c → ∞ and ultra-relativistic c → 0 limits of the κ-deformed symmetries and corresponding spacetime in (3+1) dimensions, with and without a cosmological constant. We apply the theory of Lie bialgebra contractions to the Poisson version of the κ-(A)dS quantum algebra, and quantize the resulting contracted Poisson–Hopf algebras, thus giving rise to the κ-deformation of the Newtonian (Newton–Hooke and Galilei) and Carrollian (Para-Poincare, Para-Euclidean and Carroll) quantum symmetries, including their deformed quadratic Casimir operators. The corresponding κ-Newtonian and κ-Carrollian noncommutative spacetimes are also obtained as the non-relativistic and ultra-relativistic limits of the κ-(A)dS noncommutative spacetime. These constructions allow us to analyze the non-trivial interplay between the quantum deformation parameter κ, the curvature parameter η and the speed of light parameter c.

中文翻译：

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κ-牛顿和κ-卡罗尔代数及其非对易时空

摘要 我们推导出 κ 变形对称性的非相对论 c → ∞ 和超相对论 c → 0 极限，以及 (3+1) 维的相应时空，有和没有宇宙学常数。我们将李双代数收缩理论应用于 κ-(A)dS 量子代数的泊松版本，并量化由此产生的收缩泊松-霍普夫代数，从而产生牛顿（牛顿-胡克和伽利略）的 κ-变形) 和 Carrollian（Para-Poincare、Para-Euclidean 和 Carroll）量子对称性，包括它们的变形二次 Casimir 算子。相应的κ-牛顿和κ-卡罗尔非对易时空也作为κ-(A)dS 非对易时空的非相对论和超相对论极限得到。