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ON THE COHOMOLOGY OF GENERALIZED RESTRICTED LIE ALGEBRAS 被引量:3
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作者 SHU BIN (Institute of Applied Mathematics & Physics, Shanghai Maritime University, Shanghai 200135, China.) 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 1998年第4期421-432,共12页
In [21], generalized restricted Lie algebras, defined over a field F of positive characteristic p, were introduced. In this note their cohomology, especially the so-called generalized restricted cohomology is studies.... In [21], generalized restricted Lie algebras, defined over a field F of positive characteristic p, were introduced. In this note their cohomology, especially the so-called generalized restricted cohomology is studies. Some reduction properties are obtained. For graded Cartan type Lie algebras the author determines the first Lie-cohomology groups and the first generalized restricted cohomology groups with the coefficients in the highest weight modules from which all irreducible generalized restricted modules are derived. 展开更多
关键词 generalized restricted lie algebras generalized restricted Cohomology lie algebras of Cartan type
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The double Ringel-Hall algebra on a hereditary abelian finitary length category
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作者 DOU RuJing LIU QunHua XIAO Jie 《Science China Mathematics》 SCIE 2011年第2期381-397,共17页
In this paper, we study the category H (ρ) of semi-stable coherent sheaves of a fixed slope ρ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category.... In this paper, we study the category H (ρ) of semi-stable coherent sheaves of a fixed slope ρ over a weighted projective curve. This category has nice properties: it is a hereditary abelian finitary length category. We will define the Ringel-Hall algebra of H (ρ) and relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type theorem to describe the indecomposable objects in this category, i.e. the indecomposable semi-stable sheaves. 展开更多
关键词 Ringei-Hall algebra generalized Kac-Moody lie algebra coherent sheaf semi-stability
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