• Corpus ID: 119327001

An algebraic semi-automated proof of the fundamental identity of Jordan algebras

@article{Wetering2018AnAS,
  title={An algebraic semi-automated proof of the fundamental identity of Jordan algebras},
  author={John van de Wetering},
  journal={arXiv: Rings and Algebras},
  year={2018}
}
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 self-contained 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. 
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