Twisted Lie algebras by invertible derivations

TL;DR

This paper introduces a new algebraic structure called InvDer algebra, created by twisting existing algebras with invertible derivations, and explores their relations with other algebraic systems using Rota-Baxter and endomorphism operators.

Contribution

It defines InvDer algebras and related structures, expanding the theory of algebraic twisting via invertible derivations and their connections to Rota-Baxter operators.

Findings

Defined InvDer Lie, zinbiel, and dendriform algebras

Established relations between InvDer structures and Rota-Baxter operators

Explored properties of invertible derivations in algebraic twisting

Abstract

In this paper, we introduce an algebra structure denoted by InvDer algebra whose which we twist an algebra thanks to an invertible derivation, where its inverse is also a derivation. We define InvDer Lie algebras, InvDer associated algebras, InvDer zinbiel algebras and InvDer dendriforme algebras. We also study the relations between these structures using the Rota-Baxter operators and the endomorphism operators.