Graded Contractions of Affine Kac-Moody Algebras

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.

23 pages, Ams-TeX

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Cited by in corpus (5)

• Contractions of Low-Dimensional Lie Algebras
• Graded contractions of the Gell-Mann graded sl(3,C)
• Generic graded contractions of Lie algebras
• Graded contractions on the orthogonal Lie algebras of dimensions 7 and 8
• Contractions from Grading