An embedding of the Poincaré Lie algebra into an extension of the Lie field of SO0(1,4)

Abstract

The * isomorphism between algebraic extensions of the Lie fields of SO0(1,4) and the Poincaré group are considered herein. It is shown that the principal series of unitary ray representations of SO0(1,4) are associated, via the * isomorphism, with real mass, positive and negative energy representations of the Poincaré Lie algebra with arbitrary spin. Results on the most degenerate exceptional series of SO0(1,4) representations are also given.