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

Abstract

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(n) 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.