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arXiv · 1809.02222

Derivations of octonion matrix algebras

Harry Petyt
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Abstract

It is well-known that the exceptional Lie algebras $\mathfrak{f}_4$ and $\mathfrak{g}_2$ arise from the octonions as the derivation algebras of the $3\times3$ hermitian and $1\times1$ antihermitian matrices, respectively. Inspired by this, we compute the derivation algebras of the spaces of hermitian and antihermitian matrices over an octonion algebra in all dimensions.

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Harry Petyt. 2020-04-17. Derivations of octonion matrix algebras. https://arxiv.org/abs/1809.02222

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