LEFT-SYMMETRIC ALGEBRAS FOR gl(n)
نویسنده
چکیده
We study the classification problem for left-symmetric algebras with commutation Lie algebra gl(n) in characteristic 0. The problem is equivalent to the classification of étale affine representations of gl(n). Algebraic invariant theory is used to characterize those modules for the algebraic group SL(n) which belong to affine étale representations of gl(n). From the classification of these modules we obtain the solution of the classification problem for gl(n). As another application of our approach, we exhibit left-symmetric algebra structures on certain reductive Lie algebras with a one-dimensional center and a non-simple semisimple ideal.
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