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Mat. Sb., 2000, Volume 191, Number 8, Pages 69–88 (Mi msb499)  

This article is cited in 12 scientific papers (total in 12 papers)

Deformations of classical Lie algebras

M. I. Kuznetsov, N. G. Chebochko

N. I. Lobachevski State University of Nizhni Novgorod

Abstract: For a classical Lie algebra $L$ of characteristic $p>2$ and different from $C_2$ it is proved that $H^2(L,L)=0$ when $p=3$. A classical Lie algebra is understood to be the Lie algebra of a simple algebraic group, or its quotient algebra by the centre, or a Lie algebra $A_l^z$ with $l+1\equiv 0(p)$ or $E_6^z$ when $p=3$.

DOI: https://doi.org/10.4213/sm499

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English version:
Sbornik: Mathematics, 2000, 191:8, 1171–1190

Bibliographic databases:

UDC: 512.554.31
MSC: Primary 17B56, 17B70, 17B20; Secondary 17B10
Received: 21.10.1999

Citation: M. I. Kuznetsov, N. G. Chebochko, “Deformations of classical Lie algebras”, Mat. Sb., 191:8 (2000), 69–88; Sb. Math., 191:8 (2000), 1171–1190

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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. N. G. Chebochko, “Deformations of classical Lie algebras with homogeneous root system in characteristic two. I”, Sb. Math., 196:9 (2005), 1371–1402  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Viviani, F, “Infinitesimal deformations of restricted simple Lie algebras I”, Journal of Algebra, 320:12 (2008), 4102  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    3. D. V. Reshetnikov, “Calculation of cohomology groups of the Lie algebras of series $B_n$ and $C_n$”, Russian Math. (Iz. VUZ), 53:8 (2009), 58–59  mathnet  crossref  mathscinet  zmath
    4. Bouarroudj S., Grozman P., Lebedev A., Leites D., “Divided Power (Co)Homology. Presentations of Simple Finite Dimensional Modular Lie Superalgebras with Cartan Matrix”, Homology Homotopy and Applications, 12:1 (2010), 237–278  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    5. Chebochko N.G., “Deformatsii klassicheskikh algebr li tipa d _{l} nad polem kharakteristiki 2”, Trudy NGTU im. R.E. Alekseeva, 2011, no. 1, 337–337  elib
    6. Viviani F., “Restricted Infinitesimal Deformations of Restricted Simple Lie Algebras”, J. Algebra. Appl., 11:5 (2012), 1250091  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    7. Sh. Sh. Ibraev, “O tsentralnykh rasshireniyakh klassicheskikh algebr Li”, Sib. elektron. matem. izv., 10 (2013), 450–453  mathnet
    8. Sh. Sh. Ibraev, “On the First Cohomology of an Algebraic Group and Its Lie Algebra in Positive Characteristic”, Math. Notes, 96:4 (2014), 491–498  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. Bouarroudj S., Grozman P., Lebedev A., Leites D., Shchepochkina I., “New Simple Lie Algebras in Characteristic 2”, Int. Math. Res. Notices, 2016, no. 18, 5695–5726  crossref  mathscinet  isi  scopus
    10. Chebochko N.G. Kuznetsov M.I., “Integrable cocycles and global deformations of Lie algebra of type G _{2} in characteristic 2”, Commun. Algebr., 45:7 (2017), 2969–2977  crossref  mathscinet  zmath  isi  scopus
    11. M. I. Kuznetsov, A. V. Kondrateva, N. G. Chebochko, “Prostye $14$-mernye algebry Li v kharakteristike $2$”, Voprosy teorii predstavlenii algebr i grupp. 32, Zap. nauchn. sem. POMI, 460, POMI, SPb., 2017, 158–167  mathnet
    12. Bouarroudj S., Krutov A., Leites D., Shchepochkina I., “Non-Degenerate Invariant (Super)Symmetric Bilinear Forms on Simple Lie (Super)Algebras”, Algebr. Represent. Theory, 21:5 (2018), 897–941  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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