The orthogonality relation classifies finite-dimensional formally real simple Jordan algebras

Abstract

It is shown that a finite-dimensional formally real simple Jordan algebra is completely determined by the relation of Jordan-orthogonality.

Communicated by Prof. Alberto Elduque

Keywords:

• Clique number
• formally real Jordan algebras
• Graph
• Zeros of Jordan product

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 17C55
• 15A99
• 05C15

Acknowledgments

The authors are thankful to the referee for pointing out the missing argument in the original draft (that multiplicities of the eigenvalues are also preserved under Jordan automorphisms in the cases $\mathcal{A}\in \left\{H_n\right(\mathbb{H}),H_3(\mathbb{O}\left)\right\}$) and for offering the solution. The authors would also like to thank the referee for providing some new references.

Additional information

Funding

The authors acknowledge the financial support from the Slovenian Research Agency (research core funding No. P1-0222 and No. P1-0288).