Multiloop realization of extended affine Lie algebras and Lie tori

Allison, Bruce; Berman, Stephen; Faulkner, John; Pianzola, Arturo

doi:10.1090/S0002-9947-09-04828-4

Multiloop realization of extended affine Lie algebras and Lie tori
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by Bruce Allison, Stephen Berman, John Faulkner and Arturo Pianzola PDF

Trans. Amer. Math. Soc. 361 (2009), 4807-4842 Request permission

Abstract:

An important theorem in the theory of infinite dimensional Lie algebras states that any affine Kac-Moody algebra can be realized (that is to say constructed explicitly) using loop algebras. In this paper, we consider the corresponding problem for a class of Lie algebras called extended affine Lie algebras (EALAs) that generalize affine algebras. EALAs occur in families that are constructed from centreless Lie tori, so the realization problem for EALAs reduces to the realization problem for centreless Lie tori. We show that all but one family of centreless Lie tori can be realized using multiloop algebras (in place of loop algebras). We also obtain necessary and sufficient conditions for two centreless Lie tori realized in this way to be isotopic, a relation that corresponds to isomorphism of the corresponding families of EALAs.

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