| ON THE COHOMOLOGY OF GENERALIZED RESTRICTED LIE ALGEBRAS |
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| 作者姓名： | Shu Bin |
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| 作者单位： | InstjtuteofAppliedMathematjcs＆Physjcs,ShanghaiMaritimeUniversity,Shanghai200135,China |
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| 摘 要： | 0.IntroductionThispaperisaimedatdevelopingthecohomologytheoryofmodularLiealgebrasandthendeterminingthefirstcohomologygroupsofCartantypeLiealgebras.AsgeneralizationoftheconceptofrestrictedLiealgebras,ageneralizedrestrictedLiealgebra(GRLiealgebra)wasintroducedin21],whichisassociatedwithabasisandamappingofthebasisintotheLiealgebrasatisfyingthegeneralized-restrictednessconditions.Generalizedrestrictedrepresentations(GRrepresentations)werethenintroduced,whichcanbereducedtotherepresentationsofa…
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| 关 键 词： | 广义有限 李代数 上同调 嘉当型 |
| 收稿时间： | 1996/8/16 0:00:00 |
| 修稿时间： | 1997/4/28 0:00:00 |
ON THE COHOMOLOGY OF GENERALIZED RESTRICTED LIE ALGEBRAS |
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| Shu Bin.ON THE COHOMOLOGY OF GENERALIZED RESTRICTED LIE ALGEBRAS[J].Chinese Annals of Mathematics,Series B,1998,19(4):421-432. |
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| Authors: | Shu Bin |
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| Institution: | Institute of Applied Mathematics \& Physics, Shanghai Maritime
University, Shanghai 200135, China |
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| Abstract: | 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. |
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| Keywords: | Generalized restricted Lie algebras Generalized restricted Cohomology Lie algebras of Cartan type |
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