Cohomology of reductive modular Lie algebras
-
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
-
[1] {1}KAC V, WEISFEILER B. Coadjoint action of a semisimple algebraic group and the center of the enveloping algebra in characteristic p[J]. Indag Math, 1976, 38: 136-151.{2}FRIEDLANDER E M, PARSHALL B. Modular representation theory of Lie algebras[J]. Amer J Math, 1988, 110: 1055-1093.{3}JANTZEN J C. Representations of Lie algebras in prime characteristic[C]// Proceedings of Representation Theories and Algebraic Geometry, Montreal: NATO ASI, 1997.{4}ANDERSEN H H, JANTZEN J C, SOERGEL W. Representations of quantum groups at a $p$-th root of unity and of semisimple groups in charactertic $p$:independence of $p$[J]. Asterisque, 1994, 220: 1-320.{5}LI Y Y, SHU B. Filtrations in modular representations of reductive Lie algebras[J]. Algebra Colloquium, 2010, 17(2): 265-282.{6}FRIEDLANDER E M, PARSHALL B. Deformations of Lie algebra representations[J]. Amer J Math, 1990, 112: 375-395.
点击查看大图
计量
- 文章访问数: 2426
- HTML全文浏览量: 12
- PDF下载量: 297
- 被引次数: 0