Twisted Lie algebras by invertible derivations

Abstract

In this paper, we introduce an algebra structure denoted by InvDer algebra in which we twist an algebra with an invertible derivation whose inverse is also a derivation. We define InvDer Lie algebras, InvDer associative algebras, InvDer Zinbiel algebras and InvDer dendriforme algebras. We also study the relations between these structures by using Rota–Baxter operators and endomorphism operators.