About the non-relativistic structure of the conformal algebra

A new basis of the conformal algebra is proposed, which makes appear two conjugated Schrödinger algebras. This basis allows to exhibit a chain which does not contain the Poincaré algebra, between theI (4, 2) algebra and the (two-dimensional) extended Galilean one. This non-relativistic structure of the conformal algebra is well adapted to discuss some extreme models of hadrons based on collinear massless particles.