On a variety of Lie-admissible algebras

Year 2025, Volume: 37 Issue: 37, 1 - 13, 14.01.2025

Alberto Facchini

https://doi.org/10.24330/ieja.1607238

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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