Geodesic
Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2
Journal of the European Mathematical Society, Tome 16 (2014) no. 2, pp. 327-385.

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Let Mn​ 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 M1​ 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 M1​. In this paper, we classify the algebras in M2​, and further determine the relationship between M2​ 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.
DOI : 10.4171/jems/435
Classification : 17-XX, 00-XX
Keywords: Loop algebras, multiloop algebras, extended affine Lie algebras 
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Bruce Allison; Stephen Berman; Arturo Pianzola. Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2. Journal of the European Mathematical Society, Tome 16 (2014) no. 2, pp. 327-385. doi : 10.4171/jems/435. http://geodesic.mathdoc.fr/articles/10.4171/jems/435/

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