| 在特征数0的代数闭域上半单纯代数群的上同调群 |
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| 引用本文： | 邱森.在特征数0的代数闭域上半单纯代数群的上同调群[J].华东师范大学学报(自然科学版),1987(2). |
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| 作者姓名： | 邱森 |
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| 作者单位： | 华东师范大学数学系 |
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| 摘 要： | 设G是特征数O的代数闭域k上的半单纯代数群。本文将计算系数在不可约有理G-模中G的上同调群的问题归结为计算幂零李代数的上同调群的问题。我们得到了关于H~*(G,V)的一些性质和它的维数估计式,其中V是不可约有理G-模。结果表明特征数0和特征数p>0的情况是不相同的。
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| 关 键 词： | 上同调群 半单李代数 半单代数群 维数估计 |
The Cohomology of Seml-simple Algebraic Groups Over an Algebraically Closed Field of Characteristic 0 |
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| QIU SEB.The Cohomology of Seml-simple Algebraic Groups Over an Algebraically Closed Field of Characteristic 0[J].Journal of East China Normal University(Natural Science),1987(2). |
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| Authors: | QIU SEB |
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| Institution: | QIU SEB Department of Mathematics |
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| Abstract: | Let G be a semi-simple algebraic group over an algebraically closed field k of characteristic 0.The computation of the cohomology of G with coefficients in an irreduc- ible G-module is reduced to the computation of the cohomology of the nilpotent Lie algebra.An estimate of dimension of H~*(G,V)and its properties are obtained,where V is an irreducible rational G-module.H~*(SL_2,V)and Ext_((SL)_2)~*(V,V')can be calculated when V and V' are irreducible rational SL_2-modules.The results show that the cases of characteristic 0 are different from the cases of characteristic P>0. |
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| Keywords: | cohomology semi-simple Lie algebra dimension estimate semisimple algebraic group |
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