| Quadratic Algebras of Type AIII(Ⅰ) |
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| 引用本文： | 张贺春.Quadratic Algebras of Type AIII(Ⅰ)[J].清华大学学报,1998(4). |
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| 作者姓名： | 张贺春 |
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| 作者单位： | Jakobsen H.，Jensen A.，Jndrup S.，Zhang Hechun Department of Mathematics，University of Copenhagen，DK\|2100 Denmark; Department of Applied Mathematics，Tsinghua University，Beijing 100084 |
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| 基金项目： | Supported by the National Natural Science Foundationof China(No.194 0 10 2 1) |
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| 摘 要： | IntroductionLetg=su(m,n)CbethesimplecomplexLiealgebraoftypeAr;r 1=m n.ThisistheLiealgebracorrespondingtotheHermitiansymmetricspaceoftypeAIII.Letkdenoteamaximalcompactsubalgebraofg,i.e.,k≡s(u(m)×u(n))C.ThenitisacrucialfactinrelationtoanalysisontheHermitiansymmetricspacethatthereexistsadecompositiong=p-kp (1)oftheLiealgebraintoasumofsubalgebrasandwhere,furthermore,p±areabeliank-modules.Thisleadstoadecompositiononthelevelofenvelopingalgebras,U(g)=U(p-).U(k).U(p )(2)andagooddealoftheanal…
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