Graded Contractions of Affine Kac-Moody Algebras

Details Graded Contractions of Affine Kac-Moody Algebras Graded Contractions of Affine Kac-Moody Algebras

1995-12-20

arxiv.org/abs/q-alg/9512020v1

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, Ams-TeX

Scientific paper

10.1088/0305-4470/29/14/025

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 In\"on\"u-Wigner contractions. The example of $\hat A_2$ is discussed in detail.

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