# A generalization of the Kantor-Koecher-Titsconstruction 1

@article{Palmkvist2008AGO,
title={A generalization of the Kantor-Koecher-Titsconstruction 1},
author={Jakob Palmkvist},
journal={Journal of Generalized Lie Theory and Applications},
year={2008},
volume={2},
pages={226-230}
}
• 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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