2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/19438In linear elasticity, we decompose the elasticity tensor into two irreducible pieces with 15 and 6 independent components, respectively. The {\it vanishing} of the piece with 6 independent components corresponds to the Cauchy relations. Thus, for the first time, we recognize the group-theoretical underpinning of the Cauchy relations.9 pages latex with Kluwer style files, will appear in the J. of ElasticityCondensed MatterMathematical Physicstext