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

Bruce Allison; Stephen Berman; Arturo Pianzola

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 2, page 327-385
- ISSN: 1435-9855

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topAllison, 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 -

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