Derivations of octonion matrix algebras

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 $3\times 3$ hermitian and $1\times 1$ 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.

v2: Updated references. 7 pages