On a variety of Lie-admissible algebras

Abstract

The aim of this paper is to propose the study of a class of Lie-admissible algebras. It is the class (variety) of all the (not-necessarily associative) algebras $M$ over a commutative ring $k$ with identity $1_k$ for which $(x,y,z)=(y,x,z)+(z,y,x)$ for every $x,y,z\in M$. Here $(x,y,z)$ denotes the associator of $M$. We call such algebras algebras of type $\mathcal{V}_2$. Very little is known about these algebras.

Keywords

• Lie-admissible algebra
• pre-Lie algebra
• $~$

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