  Some features of Cayley algebras (or algebras of octonions) and their Lie
algebras of derivations over fields of low characteristic are presented. More
specifically, over fields of characteristic $7$, explicit embeddings of any
twisted form of the Witt algebra into the simple split Lie algebra of type
$G_2$ are given. Over fields of characteristic $3$, even though the Lie algebra
of derivations of a Cayley algebra is not simple, it is shown that still two
Cayley algebras are isomorphic if and only if their Lie algebras of derivations
are isomorphic. Finally, over fields of characteristic $2$, it is shown that
the Lie algebra of derivations of any Cayley algebra is always isomorphic to
the projective special linear Lie algebra of degree four. The twisted forms of
this latter algebra are described too.
