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.

引用

页码：491 / 498

页数：8

共 50 条

[31] COHOMOLOGY FOR THE LIE ALGEBRA OF TYPE A2 OVER A FIELD OF CHARACTERISTIC 2
Ibraev, Sh Sh
Turbayev, B. T.
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2021, 18 : 729 - 739
[32] COHOMOLOGY ALGEBRA OF THE INFINITE SYMMETRIC GROUP AND DICKSON CHARACTERISTIC CLASSES
HUNG, NHV
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1983, 297 (12): : 611 - 614
[33] Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic Classes
Jian Qiu
Maxim Zabzine
Communications in Mathematical Physics, 2010, 300 : 789 - 833
[34] The first Chevalley-Eilenberg Cohomology group of the Lie algebra on the transverse bundle of a decreasing family of foliations
Lebtahi, Leila
JOURNAL OF GEOMETRY AND PHYSICS, 2010, 60 (12) : 2011 - 2023
[35] Generalized Levi factor actions on the Lie algebra of an algebraic group
Barry, MJJ
JOURNAL OF ALGEBRA, 1997, 195 (02) : 548 - 557
[36] LIFTING OF REPRESENTATIONS OF LIE-ALGEBRA OF A LINEAR ALGEBRAIC GROUP
MEDEN, F
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1975, 280 (23): : 1613 - 1616
[37] Algebraic group actions in the cohomology theory of Lie algebras of Cartan type
Lin, ZZ
Nakano, DK
JOURNAL OF ALGEBRA, 1996, 179 (03) : 852 - 888
[38] THE FIRST COHOMOLOGY GROUP OF THE TRIVIAL EXTENSION OF A MONOMIAL ALGEBRA
Cibils, Claude
Julia Redondo, Maria
Saorin, Manuel
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2004, 3 (02) : 143 - 159
[39] The first cohomology group of the generalized Morava stabilizer algebra
Nakai, H
Ravenel, DC
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (05) : 1629 - 1639
[40] ALGEBRAIC LIE ALGEBRA BUNDLES AND DERIVATIONS OF LIE ALGEBRA BUNDLES
Monica, M., V
Rajendra, R.
INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA, 2024, 35 : 95 - 107

← 1 2 3 4 5 →