Weakly Associative Groups
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The space ℝ c 3 of 3-dimensional relativistically admissible velocities possesses (i) a binary operation which represents the relativistic velocity composition law; and (ii) a mapping from the cartesian product ℝ c 3 ×ℝ c 3 into a subgroup of its automorphism group, Aut(ℝ c 3 ), representing the Thomas precession of special relativity. These binary operation and mapping are studied in special relativity as two isolated phenomena. It was recently discovered, however, that they are linked by an algebraic structure which gives rise to a theory of weakly associative and weakly associative-commutative groups. The axioms of these groups are presented in this paper and employed to obtain various interesting results. The algebraic structure underlying these nonstandard groups has been discovered and studied in a totally different context by Karzel (1965), Kerby and Wefelscheid.
KeywordsSpecial Relativity Binary Operation Semidirect Product Identity Automorphism Thomas Precession
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