Let be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to -tuples of commuting finite order automorphisms. It is a classical result that 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 . In this paper, we classify the algebras in , and further determine the relationship between 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.
Cite this article
Arturo Pianzola, Bruce Allison, Stephen Berman, Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2. J. Eur. Math. Soc. 16 (2014), no. 2, pp. 327–385DOI 10.4171/JEMS/435