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.
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