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Abstract: An important theorem in the theory of infinite dimensional Lie algebrasstates that any affine Kac-Moody algebra can be realized that is to sayconstructed explicitly using loop algebras. In this paper, we consider thecorresponding problem for a class of Lie algebras called extended affine Liealgebras EALAs that generalize affine algebras. EALAs occur in families thatare constructed from centreless Lie tori, so the realization problem for EALAsreduces to the realization problem for centreless Lie tori. We show that allbut one family of centreless Lie tori can be realized using multiloop algebrasin place of loop algebras. We also obtain necessary and sufficient for twocentreless Lie tori realized in this way to be isotopic, a relation thatcorresponds to isomorphism of the corresponding families of EALAs.



Author: Bruce Allison, Stephen Berman, John Faulkner, Arturo Pianzola

Source: https://arxiv.org/







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