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.
