The isometry group of n-dimensional einstein gyrogroup

Abstract

© Springer Nature Switzerland AG 2020. The space of n-dimensional relativistic velocities normalized to c = 1, (Formula Presented) is naturally associated with Einstein velocity addition (Formula Presented), which induces the rapidity metric dE on B given by (Formula Presented). This metric is also known as the Cayley–Klein metric. We give a complete description of the isometry group of (B, dE), along with its composition law.