Alberta Thy 32-95 Graded Contractions of Affine Kac-moody Algebras
نویسنده
چکیده
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 Â2 is discussed in detail. PACS numbers: 02.20.+b, 11.30.–j
منابع مشابه
Inönü - Wigner Contraction of Kac-Moody Algebras
We discuss Inönü-Wigner contractions of affine Kac-Moody algebras. We show that the Sugawara construction for the contracted affine algebra exists only for a fixed value of the level k, which is determined in terms of the dimension of the uncontracted part of the starting Lie algebra, and the quadratic Casimir in the adjoint representation. Further, we discuss contractions of G/H coset spaces, ...
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