Hom-Lie algebras are non-associative, non-commutative algebras generalizing Lie algebras by twisting the Jacobi identity by a homomorphism. The main examples are algebras of twisted derivations (i.e., linear maps with a generalized Leibniz rule). Such generalized derivations appear in all parts of number theory, so hom-Lie algebras appear to have a natural role to play in many number-theoretica...