标题： 相对论李代数展开：从伽利略到庞加莱 显示英文标题

标题： The relativistic Lie algebra expansion: from Galilei to Poincare

摘要： 我们将最近用于(2+1)维运动学代数的李代数展开方法扩展到(3+1)维伽利略代数的展开。 其中一种展开是从(3+1)维伽利略代数到洛伦兹代数；此过程在世界线的空间中引入一个等于$-1/c^2$的曲率，其中c是相对论常数。 因此，这种展开在李代数层面上逆转了从洛伦兹群到伽利略代数的非相对论收缩$c\to \infty$。 伽利略代数允许另一种自然展开到牛顿-霍克代数；这些展开恢复了一个非零的时空曲率$\pm 1/\tau^2$，其中$\tau$是牛顿-霍克宇宙的时间半径，也使用相同的方法进行了研究。 显示英文摘要

摘要： We extend a Lie algebra expansion method recently introduced for the (2+1)-dimensional kinematical algebras to the expansions of the (3+1)-dimensional Galilei algebra. One of these expansions goes from the (3+1)-dimensional Galilei algebra to the Poincare one; this process introduces a curvature equal to $-1/c^2$, where c is the relativistic constant, in the space of worldlines. This expansion therefore reverses, at the Lie algebra level, the non-relativistic contraction $c\to \infty$ from the Poincare group to the Galilei one. The Galilei algebra allows another natural expansion to the Newton-Hooke algebras; these expansions which recover a non-zero spacetime curvature $\pm 1/\tau^2$, where $\tau$ is the Newton-Hooke universe time radius, are also studied by using the same method.