标题： 一种新的李代数展开方法：伽利略展开到洛伦兹和牛顿-霍克 显示英文标题

标题： A new Lie algebra expansion method: Galilei expansions to Poincare and Newton-Hooke

摘要： 我们修改了一种最近为(2+1)维运动学代数引入的李代数展开方法，以便适用于更高维度。这种改进且几何化的程序被用于展开(3+1)维伽利略代数，并导致其物理上有意义的“扩展”邻域。一种展开引入了庞加莱代数，在世界线的平坦伽利略空间中引入了一个曲率$-1/c^2$，同时保持平坦时空，在此过程中时间从绝对变为相对。这在李代数层面上形式上逆转了众所周知的非相对论收缩$c\to \infty$，该收缩从庞加莱群到伽利略群；这种展开是以显式构造的方式进行的。另一种可能的展开导致牛顿-霍克代数，在时空中引入了一个非零的时空曲率$\pm 1/\tau^2$，同时保持世界线的平坦空间。 显示英文摘要

摘要： We modify a Lie algebra expansion method recently introduced for the (2+1)-dimensional kinematical algebras so as to work for higher dimensions. This new improved and geometrical procedure is applied to expanding the (3+1)-dimensional Galilei algebra and leads to its physically meaningful `expanded' neighbours. One expansion gives rise to the Poincare algebra, introducing a curvature $-1/c^2$ in the flat Galilean space of worldlines, while keeping a flat spacetime which changes from absolute to relative time in the process. This formally reverses, at a Lie algebra level, the well known non-relativistic contraction $c\to \infty$ that goes from the Poincare group to the Galilei one; this expansion is done in an explicit constructive way. The other possible expansion leads to the Newton-Hooke algebras, endowing with a non-zero spacetime curvature $\pm 1/\tau^2$ the spacetime, while keeping a flat space of worldlines.