Decompositions in categories of highest weight modules
نویسندگان
چکیده
منابع مشابه
Highest Weight Categories and Recollements
We provide several equivalent descriptions of a highest weight category using recollements of abelian categories. Also, we explain the connection between sequences of standard and exceptional objects.
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Let G be a semisimple, simply connected algebraic group defined over an algebraically closed field k of positive characteristic p. Assume that p is larger than the Coxeter number of G and that the Lusztig character formula holds for regular restricted dominant weights. In this paper, we introduce two new highest weight categories C even and C reg odd , both full subcategories of the category C ...
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We prove that for simple complex finite dimensional Lie algebras, affine Kac-Moody Lie algebras, the Virasoro algebra and the Heisenberg-Virasoro algebra, simple highest weight modules are characterized by the property that all positive root elements act on these modules locally nilpotently. We also show that this is not the case for higher rank Virasoro and for Heisenberg algebras.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1986
ISSN: 0021-8693
DOI: 10.1016/0021-8693(86)90083-9