Highest-weight theory for truncated current Lie algebras
نویسندگان
چکیده
منابع مشابه
Highest-weight Theory for Truncated Current Lie Algebras
Let g be a Lie algebra over a field k of characteristic zero, and a fix positive integer N. The Lie algebra ĝ = g ⊗k k[t]/t N+1 k[t] is called a truncated current Lie algebra. In this paper a highest-weight theory for ĝ is developed when the underlying Lie algebra g possesses a triangular decomposition. The principal result is the reducibility criterion for the Verma modules of ĝ for a wide cla...
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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....
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2011
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2011.04.015