On the first cohomology of an algebraic group and its Lie algebra in positive characteristic

被引：0
|
作者：
Ibraev, Sh. Sh. [1 ]
机构：
[1] Bolashak Univ, Kyzylorda, Kazakhstan
来源：
MATHEMATICAL NOTES | 2014年 / 96卷 / 3-4期
关键词：
algebraic group; Lie algebra of an algebraic group; irreducible system of roots; algebraically closed field; first cohomology group; SIMPLE MODULES; CO-HOMOLOGY; EXTENSIONS;
D O I：
10.1134/S0001434614090247
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Necessary and sufficient conditions for the first cohomology group of an algebraic group with irreducible root system over an algebraically closed field of characteristicp > 0 to be isomorphic to the corresponding first cohomology group of the Lie algebra of the group with coefficients in simple modules are obtained. The spaces of outer derivations of the classical modular Lie algebras are evaluated forp > 2.
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页码：491 / 498
页数：8
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