Integrable modules for Lie tori

In this paper we consider the universal central extension of a centerless Lie torus satisfying fgc condition and classify its irreducible integrable modules when the center acts non-trivially. These algebras (Lie tori) are naturally ZnZn-graded and we develop a one to one correspondence between their graded and non-graded modules. At the non-graded level their irreducible integrable modules turn out to be highest weight modules for the direct sum of finitely many affine Lie algebras upto an automorphism.