Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Octonions, triality, the exceptional Lie algebra F4, and polar actions
  on the Cayley hyperbolic plane   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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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: cs