TY  - JOUR
T1  - On a variety of Lie-admissible algebras
AU  - Facchini, Alberto
PY  - 2025
DA  - January
Y2  - 2024
DO  - 10.24330/ieja.1607238
JF  - International Electronic Journal of Algebra
JO  - IEJA
PB  - Abdullah HARMANCI
WT  - DergiPark
SN  - 1306-6048
SP  - 1
EP  - 13
VL  - 37
IS  - 37
LA  - en
AB  - 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.
KW  - Lie-admissible algebra
KW  - pre-Lie algebra
KW  - $~$
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UR  - https://doi.org/10.24330/ieja.1607238
L1  - https://dergipark.org.tr/en/download/article-file/4466752
ER  -