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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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  • https://doi.org/10.4213/mzm10313
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    • This publication is cited in the following 8 articles:
    1. Sofiane Bouarroudj, Pavel Grozman, Alexei Lebedev, Dimitry Leites, “Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras (with an Appendix by Andrey Krutov)”, SIGMA, 19 (2023), 032, 73 pp.  mathnet  crossref  mathscinet
    2. Ibraev Sh.S. Kainbaeva L.S. Menlikozhaeva S.K., “On Cohomology of Simple Modules For Modular Classical Lie Algebras”, Axioms, 11:2 (2022), 78  crossref  isi  scopus
    3. Sherali S. Ibraev, Larissa S. Kainbaeva, Angisin Z. Seitmuratov, “On Restricted Cohomology of Modular Classical Lie Algebras and Their Applications”, Mathematics, 10:10 (2022), 1680  crossref
    4. Ibrayeva A.A., Ibraev Sh.Sh., Yeshmurat G.K., “Cohomology of Simple Modules For Sl(3) (K) in Characteristic 3”, Bull. Karaganda Univ-Math., 103:3 (2021), 36–43  crossref  isi
    5. 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  crossref  isi
    6. Saïd Benayadi, Sofiane Bouarroudj, Mounir Hajli, “Double Extensions of Restricted Lie (Super)Algebras”, Arnold Math J., 6:2 (2020), 231  crossref
    7. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    8. Sh. Sh. Ibraev, “On the cohomology of simple restricted modules for algebraic groups”, Bull. Karaganda Univ-Math., 85:1 (2017), 51–56  isi
    Citing articles in Google Scholar: Russian citations, English citations
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