Exceptional Lie Algebras, SU(3) and Jordan Pairs Part 2: Zorn-type Representations

Alessio Marrani, Piero Truini

Published 2014-03-20, updated 2014-05-27Version 2

A representation of the exceptional Lie algebras is presented. It reflects a simple unifying view and it is realized in terms of Zorn-type matrices. The role of the underlying Jordan pair and Jordan algebra content is crucial in the development of the structure. Each algebra contains three Jordan pairs sharing the same Lie algebra of automorphisms and the same external su(3) symmetry. Applications in physics are outlined.