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

Alessio Marrani; Piero Truini

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

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arxiv 1403.5120 v2 pith:KKVKLIXA submitted 2014-03-20 math-ph hep-thmath.MP

Alessio Marrani , Piero Truini This is my paper · ORCID

classification math-phhep-thmath.MP

keywords jordanalgebraalgebrasexceptionalpairssamezorn-typeapplications

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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.

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Exceptional Periodicity and Magic Star Algebras. I : Foundations
math.RT 2019-09 conditional novelty 5.0 of 10

The paper rigorously defines 'Magic Star algebras', periodic finite dimensional generalizations of e6, e7, and e8, which are Lie algebras only at the base level n=1.

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