Equivariant hom-Lie algebras and twisted derivations on (arithmetic) schemes

In this paper we introduce the notion of global equivariant hom-Lie algebra. This is a Lie algebra-like structure associated with twisted derivations. We prove several results on the structure of modules of twisted derivations and how they form global equivariant hom-Lie algebras. Particular emphasis is put on examples and results in arithmetic geometry.