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Toroidal Lie algebras and vertex representations

✍ Scribed by Robert V. Moody; Senapathi Eswara Rao; Takeo Yokonuma

Publisher: Springer
Year: 1990
Tongue: English
Weight: 956 KB
Volume: 35
Category: Article
ISSN: 0046-5755
DOI: 10.1007/bf00147350

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✦ Synopsis

The paper describes the theory of the toroidal Lie algebra, i.e. the Lie algebra of polynomial maps of a complex torus C x x C × into a finite-dimensional simple Lie algebra g. We describe the universal central extension I of this algebra and give an abstract presentation for it in terms of generators and relations involving the extended Cartan matrix of g. Using this presentation and vertex operators we obtain a large class of integrable indecomposable representations of t in the case that g is of type A, D, or E. The submodule structure of these indecomposable modules is described in terms of the ideal structure of a suitable commutative associative algebra.

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