  Hom-Lie algebras are non-associative algebras generalizing Lie algebras by
twisting the Jacobi identity by an endomorphism. The main examples are algebras
of twisted derivations (i.e., linear maps with a generalized Leibniz rule).
Such generalized derivations seem to pop up in different guises in many parts
of number theory and arithmetic geometry. In fact, any place something like
$\mathrm{id}-\phi$, where $\phi$ is (possibly extended to) a ring morphism,
appears, such as in $p$-adic Hodge theory, Iwasawa theory, e.t.c., there is a
twisted derivation hiding. Therefore, hom-Lie algebras appear to have a natural
r\^ole to play in many number-theoretical disciplines. This paper is a first
step in a study of these operators and associated algebras in an
arithmetic-/geometric context.
