The isometry group of n-dimensional Einstein gyrogroup

2019/05/04 by Suksumran, Teerapong
#20N05 #51F25 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Metric Geometry (math.MG) #Primary 51A05 #Secondary 83A05

paper · doi:10.48550/arxiv.1905.01496

Abstract

The space of n-dimensional relativistic velocities normalized to c = 1, \mathbbB = \v∈ℝⁿ\colon ‖v‖ lt; 1\, is naturally associated with Einstein velocity addition ⊕_E, which induces the rapidity metric d_E on \mathbbB given by d_E(u, v) = \tanh^-1‖-u⊕_Ev‖. This metric is also known as the Cayley-Klein metric. We give a complete description of the isometry group of (\mathbbB, d_E), along with its composition law.

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