Abstract
Abstraction of the relativistic velocity addition law and of the Thomas rotation of the special theory of relativity yields a means of endowing the unit ball in any real inner product space with a group- like structure, in which the standard associative- commutative laws are relaxed by means of the Thomas rotation. The resulting group- like object is called a complete weakly associative- commutative groupoid. Any complete WACG can be extended to a group analogous to the Lorentz group of the special theory of relativity.
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