On a remarkable class of left-symmetric algebras and its relationship with the 
class of Novikov algebras

Guediri, Mohammed

doi:10.1080/00927872.2015.1065853

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On a remarkable class of left-symmetric algebras and its relationship with the class of Novikov algebras

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Guediri, Mohammed
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1080/00927872.2015.1065853
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Guediri, M. (2016). On a remarkable class of left-symmetric algebras and its relationship with the class of Novikov algebras. Communications in Algebra, 44(7), 2919-2937. doi:10.1080/00927872.2015.1065853.

Cite as: https://hdl.handle.net/21.11116/0000-0004-D9ED-D

Abstract

We discuss locally simply transitive affine actions of Lie groups G on finite-dimensional vector spaces such that the commutator subgroup [G,G] is acting by translations. In other words, we consider left-symmetric algebras satisfying the identity [x,y].z=0. We derive some basic characterizations of such left-symmetric algebras and we highlight their relationships with the so-called Novikov algebras and derivation algebras.