On anticommutative algebras for which $[R_a,R_b]$ is a derivation

TL;DR

This paper investigates a special class of anticommutative algebras where the commutator of any two multiplications acts as a derivation, revealing structural properties of such algebras.

Contribution

It introduces and analyzes a new class of anticommutative algebras characterized by derivation properties of commutators of multiplications.

Findings

Characterization of the algebraic structure under the derivation condition

Identification of conditions for anticommutative algebras to satisfy the property

Potential classification results for these algebras

Abstract

We study anticommutative algebras with the property that commutator of any two multiplications is a derivation.