Representations of Loop Kac-Moody Lie Algebras

We study representations of the Loop Kac-Moody Lie algebra g \otimes A, where g is any Kac-Moody algebra and A is a ring of Laurent polynomials in n commuting variables. In particular, we study representations with finite dimensional weight spaces and their graded versions. When we specialize g to be a finite dimensional or affine Lie algebra we obtain modules for toroidal Lie algebras.