Ju n 20 07 HIGHEST - WEIGHT THEORY FOR TRUNCATED CURRENT LIE ALGEBRAS
نویسنده
چکیده
is called a truncated current Lie algebra, or sometimes a generalised Takiff algebra. We shall describe a highest-weight theory for ĝ, and the reducibility criterion for the universal objects of this theory, the Verma modules. The principal motivation, beside the aesthetic, is that certain representations of affine Lie algebras are essentially representations of a truncated current Lie algebra. For example, the exp-polynomial representations of affine Lie algebras, studied by Billig, Berman and Zhao [1], [2] may be understood in this fashion.
منابع مشابه
Representations of Truncated Current Lie Algebras
Let g denote a Lie algebra, and let ĝ denote the tensor product of g with a ring of truncated polynomials. The Lie algebra ĝ is called a truncated current Lie algebra. The highest-weight theory of ĝ is investigated, and a reducibility criterion for the Verma modules is described. Let g be a Lie algebra over a field k of characteristic zero, and fix a positive integer N . The Lie algebra (1) ĝ =...
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