华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (5): 115-120,132.

• 应用数学与基础数学 • 上一篇    下一篇

简约模李代数的上同调

李宜阳   

  1. 上海工程技术大学 基础教学学院, 上海 201620
  • 收稿日期:2011-01-01 修回日期:2011-04-01 出版日期:2011-09-25 发布日期:2011-11-22

Cohomology of reductive modular Lie algebras

LI Yi-yang   

  1. School of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, China
  • Received:2011-01-01 Revised:2011-04-01 Online:2011-09-25 Published:2011-11-22

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摘要： 令\,$G$\,为素特征代数闭域上简约连通的代数群, $\mathfrak{g}$\,是\,$G$\,的李代数. 本文研究当\,$p$-特征\,$\chi$\,具有标准\,Levi\,型时简约模李代数\,$\mathfrak{g}$\,的上同调. 当\,baby Verma\,模的最高权为\,$p$-正则时, 得到了\,baby Verma\,模和扭\,baby Verma\,模之间的扩张群非分裂的充分必要条件.

关键词: 标准\, Levi\, 型, baby Verma\, 模, 上同调

Abstract: Let $G$ be a connected reductive algebraic group over an algebraically closed field $k$ of prime characteristic $p$, and $\mathfrak{g}=\mathrm{Lie}(G)$. This paper studied the cohomology of the reductive Lie algebra $\mathfrak{g}$ with $p$-character $\chi$ of standard Levi form. When the highest weight of baby Verma module is $p$-regular, the necessary and sufficient condition for the Ext groups between baby Verma module and twist baby Verma module being non-split was gotten.

Key words: standard Levi-form, baby Verma modules, cohomology

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