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Lie algebra $\mathfrak{so}(9)$ as a subalgebra of $\mathfrak{f}_4$
What are the explicit Lie algebra mono-morphisms from $\mathfrak{so}(9)$ into the exceptional Lie algebra $\mathfrak{f}_4$ and from $\mathfrak{f}_4$ to $\mathfrak{e}_6$? Are these explicitly described in any book?
