The Isometry Group of n-Dimensional Einstein Gyrogroup

Abstract

The space of n-dimensional relativistic velocities normalized to c = 1,is naturally associated with Einstein velocity addition ⊕ E , which induces the rapidity metric d E on B given by d E (u, v) = tanh −1 − u ⊕ E v . This metric is also known as the Cayley-Klein metric. We give a complete description of the isometry group of (B, d E ), along with its composition law.