A generalization of the Kantor-Koecher-Titsconstruction 1

  title={A generalization of the Kantor-Koecher-Titsconstruction 1},
  author={Jakob Palmkvist},
  journal={Journal of Generalized Lie Theory and Applications},
  • Jakob Palmkvist
  • Published 17 August 2013
  • Mathematics
  • Journal of Generalized Lie Theory and Applications
The Kantor-Koecher-Tits construction associates a Lie algebra to any Jordan algebra. We generalize this construction to include also extensions of the associated Lie algebra. In particular, the conformal realization of so(p + 1, q + 1) generalizes to so(p + n, q + n), for arbitrary n, with a linearly realized subalgebra so(p, q). We also show that the construction applied to 3 × 3 matrices over the division algebras R, C, H, O gives rise to the exceptional Lie algebras f4, e6, e7, e8, as well… 

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