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

Allison, Bruce, Berman, Stephen, and Pianzola, Arturo. "Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2." Journal of the European Mathematical Society 016.2 (2014): 327-385. <http://eudml.org/doc/277669>.

@article{Allison2014,
abstract = {Let $\mathbb \{M\}_n$ 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 $\mathbb \{M\}_1$ 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 $\mathbb \{M\}_1$. In this paper, we classify the algebras in $\mathbb \{M\}_2$, and further determine the relationship between $\mathbb \{M\}_2$ 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.},
author = {Allison, Bruce, Berman, Stephen, Pianzola, Arturo},
journal = {Journal of the European Mathematical Society},
keywords = {loop algebras; multiloop algebras; extended affine Lie algebras; loop algebras; multiloop algebras; extended affine Lie algebras},
language = {eng},
number = {2},
pages = {327-385},
publisher = {European Mathematical Society Publishing House},
title = {Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2},
url = {http://eudml.org/doc/277669},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Allison, Bruce
AU - Berman, Stephen
AU - Pianzola, Arturo
TI - Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 2
SP - 327
EP - 385
AB - Let $\mathbb {M}_n$ 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 $\mathbb {M}_1$ 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 $\mathbb {M}_1$. In this paper, we classify the algebras in $\mathbb {M}_2$, and further determine the relationship between $\mathbb {M}_2$ 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.
LA - eng
KW - loop algebras; multiloop algebras; extended affine Lie algebras; loop algebras; multiloop algebras; extended affine Lie algebras
UR - http://eudml.org/doc/277669
ER -