LINEAR FORM OF 3-SCALE SPECIAL RELATIVITY ALGEBRA AND THE RELEVANCE OF STABILITY

Abstract

We show that the algebra of the recently proposed Triply Special Relativity can be brought to a linear (i.e., Lie) form by a correct identification of its generators. The resulting Lie algebra is the stable form proposed by Vilela Mendes a decade ago, itself a reapparition, up to some important sign, of Yang's algebra, dating from 1947. As a corollary we assure that, within the Lie algebra framework, there is no Quadruply Special Relativity.