This article is cited in 8 papers

On the First Cohomology of an Algebraic Group and Its Lie Algebra in Positive Characteristic

Sh. Sh. Ibraev

Bolashak University, Kzakhstan

Abstract: 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 $p>2$.

Keywords: algebraic group, Lie algebra of an algebraic group, irreducible system of roots, algebraically closed field, first cohomology group.

UDC: 512.815.6

Received: 26.02.2013
Revised: 24.02.2014

DOI: 10.4213/mzm10313

 English version: Mathematical Notes, 2014, 96:4, 491–498

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