ON A REMARKABLE CLASS OF LEFT-SYMMETRIC ALGEBRAS AND ITS RELATIONSHIP WITH THE CLASS OF NOVIKOV ALGEBRAS

摘要

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 center dot 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.