Corpus ID: 119716819

Gradings of Lie algebras, magical spin geometries and matrix factorizations

@article{Abuaf2019GradingsOL,
  title={Gradings of Lie algebras, magical spin geometries and matrix factorizations},
  author={Roland Abuaf and Laurent Manivel},
  journal={arXiv: Algebraic Geometry},
  year={2019}
}
  • Roland Abuaf, Laurent Manivel
  • Published 2019
  • Mathematics
  • arXiv: Algebraic Geometry
  • We describe a remarkable rank fourtenn matrix factorization of the octic Spin(14)-invariant polynomial on either of its half-spin representations. We observe that this representation can be, in a suitable sense, identified with a tensor product of two octonion algebras. Moreover the matrix factorisation can be deduced from a particular Z-grading of the exceptional Lie algebra $\mathfrak{e}_8$. Intriguingly, the whole story can be extended to the whole Freudenthal-Tits magic square and yields… CONTINUE READING
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