Geodesic
On the First Cohomology of an Algebraic Group and Its Lie Algebra in Positive Characteristic
Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 512-521

Voir la notice de l'article provenant de la source Math-Net.Ru

Necessary and sufficient conditions for the first cohomology group of an algebraic group with irreducible root system over an algebraically closed field of characteristic $p>0$ 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 for $p>2$.
Mots-clés : algebraic group, Lie algebra of an algebraic group
Keywords: irreducible system of roots, algebraically closed field, first cohomology group. 
@article{MZM_2014_96_4_a3,
     author = {Sh. Sh. Ibraev},
     title = {On the {First} {Cohomology} of an {Algebraic} {Group} and {Its} {Lie} {Algebra} in {Positive} {Characteristic}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {512--521},
     publisher = {mathdoc},
     volume = {96},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a3/}
}
TY  - JOUR
AU  - Sh. Sh. Ibraev
TI  - On the First Cohomology of an Algebraic Group and Its Lie Algebra in Positive Characteristic
JO  - Matematičeskie zametki
PY  - 2014
SP  - 512
EP  - 521
VL  - 96
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a3/
LA  - ru
ID  - MZM_2014_96_4_a3
ER  - 
%0 Journal Article
%A Sh. Sh. Ibraev
%T On the First Cohomology of an Algebraic Group and Its Lie Algebra in Positive Characteristic
%J Matematičeskie zametki
%D 2014
%P 512-521
%V 96
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a3/
%G ru
%F MZM_2014_96_4_a3
Sh. Sh. Ibraev. On the First Cohomology of an Algebraic Group and Its Lie Algebra in Positive Characteristic. Matematičeskie zametki, Tome 96 (2014) no. 4, pp. 512-521. http://geodesic.mathdoc.fr/item/MZM_2014_96_4_a3/