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Matematicheskie Zametki, 2014, Volume 96, Issue 4, Pages 512–521
DOI: https://doi.org/10.4213/mzm10313 (Mi mzm10313) 		 
This article is cited in 8 scientific papers (total in 8 papers)

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

Sh. Sh. Ibraev

Bolashak University, Kzakhstan
Full-text PDF (513 kB) Citations (8)
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DOI: https://doi.org/10.4213/mzm10313
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.
Received: 26.02.2013
Revised: 24.02.2014
English version:
Mathematical Notes, 2014, Volume 96, Issue 4, Pages 491–498
DOI: https://doi.org/10.1134/S0001434614090247
Bibliographic databases:
Document Type: Article
UDC: 512.815.6
Language: Russian
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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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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