Clifford algebra-parametrized octonions and generalizations

@article{Rocha2006CliffordAO,
  title={Clifford algebra-parametrized octonions and generalizations},
  author={R. Rocha and J. Vaz and Jr.},
  journal={Journal of Algebra},
  year={2006},
  volume={301},
  pages={459-473}
}
Abstract Introducing products between multivectors of C l 0 , 7 (the Clifford algebra over the metric vector space R 0 , 7 ) and octonions, resulting in an octonion, and leading to the non-associative standard octonionic product in a particular case, we generalize the octonionic X-product, associated with the transformation rules for bosonic and fermionic fields on the tangent bundle over the 7-sphere S 7 , and the XY-product. This generalization is accomplished in the u- and ( u , v… Expand
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