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Graded Contractions of Affine Kac-Moody Algebras

Marc de Montigny
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Abstract

The method of graded contractions, based on the preservation of the automorphisms of finite order, is applied to the affine Kac-Moody algebras and their representations, to yield a new class of infinite dimensional Lie algebras and representations. After the introduction of the horizontal and vertical gradings, and the algorithm to find the horizontal toroidal gradings, I discuss some general properties of the graded contractions, and compare them with the Inönü-Wigner contractions. The example of $\hat A_2$ is discussed in detail.

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BibTeXRIS

Marc de Montigny. 1995-12-20. Graded Contractions of Affine Kac-Moody Algebras. https://doi.org/10.1088/0305-4470%2F29%2F14%2F025

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