An algebraic semiautomated proof of the fundamental identity of Jordan algebras
Abstract
The fundamental identity of quadratic Jordan algebras $Q_{Q_a b} = Q_aQ_bQ_a$ is commonly proven as a consequence of MacDonalds theorem or using more analytic methods. In this short note we give a selfcontained purely algebraic proof using just a few easily proven identities and a Python script that follows a simple randomised logic to reduce expressions of Jordan operators.
 Publication:

arXiv eprints
 Pub Date:
 June 2018
 arXiv:
 arXiv:1807.00164
 Bibcode:
 2018arXiv180700164V
 Keywords:

 Mathematics  Rings and Algebras
 EPrint:
 4 pages + 13 page explanation of the script and code listing