Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2

Let M_n be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to n-tuples of commuting finite order automorphisms. It is a classical result that M_1 is the class of all derived algebras modulo their centres of affine Kac-Moody Lie algebras. This combined with the Peterson-Kac conjugacy theorem for affine algebras results in a classification of the algebras in M_1. In this paper, we classify the algebras in M_2, and further determine the relationship between M_2 and two other classes of Lie algebras: the class of all loop algebras of affine Lie algebras and the class of all extended affine Lie algebras of nullity 2.