A realization of the Lie algebra associated to a Kantor triple system

Palmkvist, Jakob

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A realization of the Lie algebra associated to a Kantor triple system

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Palmkvist, Jakob
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Palmkvist, J. (2006). A realization of the Lie algebra associated to a Kantor triple system. Journal of Mathematical Physics, 47(2): 023505.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4AAD-A

Abstract

We present a nonlinear realization of the 5-graded Lie algebra associated to a Kantor triple system. Any simple Lie algebra can be realized in this way, starting from an arbitrary 5-grading. In particular, we get a unified realization of the exceptional Lie algebras [fraktur f]4,[fraktur e]6,[fraktur e]7,[fraktur e]8, in which they are respectively related to the division algebras [openface R],[openface C],[openface H],[openface O]