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

  • Bruce Allison

    University of Alberta, Edmonton, Canada
  • Stephen Berman

    Saskatoon, Canada
  • Arturo Pianzola

    University of Alberta, Edmonton, Canada

Abstract

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

Bruce Allison, Stephen Berman, Arturo Pianzola, Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2. J. Eur. Math. Soc. 16 (2014), no. 2, pp. 327–385

DOI 10.4171/JEMS/435