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 Mat. Zametki, 2014, Volume 96, Issue 4, Pages 512–521 (Mi mz10313)

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.

DOI: https://doi.org/10.4213/mzm10313

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

Bibliographic databases:

UDC: 512.815.6
Revised: 24.02.2014

Citation: Sh. Sh. Ibraev, “On the First Cohomology of an Algebraic Group and Its Lie Algebra in Positive Characteristic”, Mat. Zametki, 96:4 (2014), 512–521; Math. Notes, 96:4 (2014), 491–498

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz10313
• https://doi.org/10.4213/mzm10313
• http://mi.mathnet.ru/eng/mz/v96/i4/p512

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Sh. Sh. Ibraev, “On the Second Cohomology of an Algebraic Group and of Its Lie Algebra in a Positive Characteristic”, Math. Notes, 101:5 (2017), 841–849
2. Sh. Sh. Ibraev, “On the cohomology of simple restricted modules for algebraic groups”, Bull. Karaganda Univ-Math., 85:1 (2017), 51–56
3. Ibraev Sh.Sh., Kainbaeva L.S., Menlikhozhayeva S.K., “Cohomology of Simple Modules For Algebraic Groups”, Bull. Karaganda Univ-Math., 97:1 (2020), 37–43
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