Homogeneous Construction of the Toroidal Lie Algebra of Type A1.

In this paper, we consider an analogue of the level two homogeneous construction of the affine Kac–Moody algebra $A^{(1)}_{1}$ by vertex operators. We construct modules for the toroidal Lie algebra and the extended toroidal Lie algebra of type A1. We also prove that the module is completely reducible for the extended toroidal Lie algebra. [ABSTRACT FROM AUTHOR]