Arithmetic Witt-hom-Lie algebras

Abstract

This paper is concerned with explaining and further developing the rather technical definition of a hom-Lie algebra given in a previous paper which was an adaption of the ordinary definition to the language of number theory and arithmetic geometry. To do this we here introduce the notion of Witt-hom-Lie algebras and give interesting arithmetic applications, both in the Lie algebra case and in the hom-Lie algebra case. The paper ends with a discussion of a few possible applications of the developed hom-Lie language.