Exceptional Lie algebras, SU(3), and Jordan pairs

Piero Truini

Vol. 260 (2012), No. 1, 227–243

DOI: 10.2140/pjm.2012.260.227

Abstract

A simple unifying view of the exceptional Lie algebras is presented. The underlying Jordan pair content and role are exhibited. Each algebra contains three Jordan pairs sharing the same Lie algebra of automorphisms and the same external su(3) symmetry. Eventual physical applications and implications of the theory are outlined.

Keywords

exceptional Lie algebras, e₈, Jordan pairs, magic square

Mathematical Subject Classification 2010

Primary: 17B25

Secondary: 17C40

Milestones

Received: 29 March 2012

Accepted: 2 April 2012

Published: 11 October 2012