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arXiv · 1802.08075

Octonions, triality, the exceptional Lie algebra F4, and polar actions on the Cayley hyperbolic plane

Andreas Kollross
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Abstract

Using octonions and the triality property of Spin(8), we find explicit formulae for the Lie brackets of the exceptional simple real Lie algebras $\mathfrak{f}_4$ and $\mathfrak{f}^*_4$, i.e. the Lie algebras of the isometry groups of the Cayley projective plane and the Cayley hyperbolic plane. As an application, we classify polar actions on the Cayley hyperbolic plane which leave a totally geodesic subspace invariant.

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Andreas Kollross. 2018-02-22. Octonions, triality, the exceptional Lie algebra F4, and polar actions on the Cayley hyperbolic plane. https://arxiv.org/abs/1802.08075

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