A Series of Algebras Generalizing the Octonions and Hurwitz-Radon Identity

@article{MorierGenoud2010ASO,
  title={A Series of Algebras Generalizing the Octonions and Hurwitz-Radon Identity},
  author={Sophie Morier-Genoud and Valentin Ovsienko},
  journal={Communications in Mathematical Physics},
  year={2010},
  volume={306},
  pages={83-118}
}
We study non-associative twisted group algebras over $${(\mathbb{Z}_2)^n}$$ with cubic twisting functions. We construct a series of algebras that extend the classical algebra of octonions in the same way as the Clifford algebras extend the algebra of quaternions. We study their properties, give several equivalent definitions and prove their uniqueness within some natural assumptions. We then prove a simplicity criterion.We present two applications of the constructed algebras and the developed… CONTINUE READING

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