Left-symmetric algebras for gl(n)

We study the classification problem for left-symmetric algebras with commut ation Lie algebra gl(n) in characteristic 0. The problem is equivalent to t he classification of etale affine representations of gl(n). Algebraic invar iant theory is used to characterize those modules for the algebraic group S L(n) which belong to affine etale representations of gl(n). From the classi fication of these modules we obtain the solution of the classification prob lem for gl(n). As another application of our approach, we exhibit left-symm etric algebra structures on certain reductive Lie algebras with a one-dimen sional center and a non-simple semisimple ideal.