ABSTRACT
Einstein’s addition law of three-dimensional relativistically admissible velocities is the corner stone [125] of Einstein’s three-vector formalism of the special theory of relativity that he founded in 1905 [29, 71]. The resulting binary operation, ⊕, called Einstein addition, is employed along with the nonassociative algebraic structures that it encodes. These algebraic structures are the gyrocommutative gyrogroup structure, studied in this chapter, and the gyrovector space structure, studied in Chapter 3. It will turn out that Einstein gyrovector spaces form the algebraic setting for the n-dimensional Cartesian-Beltrami-Klein ball model of
the standard n-dimensional Cartesian model of analytic Euclidean geometry.
