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Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 4, Pages 762–788 (Mi izv2052)  

This article is cited in 14 scientific papers (total in 14 papers)

Exponentials in Lie algebras of characteristic $p$

B. Yu. Weisfeiler, V. G. Kac


Abstract: The relationship between the structure of a simple Lie algebra of finite characteristic and the structure of the group of its automorphisms is investigated. The results obtained are used to classify simple Lie algebras of characteristic $p>5$ for which the largest reduced subgroup in the scheme of automorphisms is a maximal subscheme. An analogous classification theorem is proved for “simple” group schemes, i.e. schemes every normal divisor of which lying in the reduced subscheme is the kernel of some purely nonseparable isogeny. For characteristics 2 and 3, families of counterexamples are constructed to all results obtained for $p>5$.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:4, 777–803

Bibliographic databases:

UDC: 519.46
MSC: Primary 17B20, 17B05, 14L15; Secondary 17B10, 17B45
Received: 10.07.1970

Citation: B. Yu. Weisfeiler, V. G. Kac, “Exponentials in Lie algebras of characteristic $p$”, Izv. Akad. Nauk SSSR Ser. Mat., 35:4 (1971), 762–788; Math. USSR-Izv., 5:4 (1971), 777–803

Citation in format AMSBIB
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\by B.~Yu.~Weisfeiler, V.~G.~Kac
\paper Exponentials in Lie algebras of characteristic~$p$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 4
\pages 762--788
\mathnet{http://mi.mathnet.ru/izv2052}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=306282}
\zmath{https://zbmath.org/?q=an:0245.17007|0252.17003}
\transl
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 4
\pages 777--803
\crossref{https://doi.org/10.1070/IM1971v005n04ABEH001116}


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    Erratum

    This publication is cited in the following articles:
    1. V. G. Kats, “Globalnye psevdogruppy Kartana i prostye algebry Li kharakteristiki $p$”, UMN, 26:3(159) (1971), 199–200  mathnet  mathscinet  zmath
    2. V. G. Kac, “Description of filtered Lie algebras with which graded Lie algebras of Cartan type are associated”, Math. USSR-Izv., 8:4 (1974), 801–835  mathnet  crossref  mathscinet  zmath
    3. V.G Kac, “Lie superalgebras”, Advances in Mathematics, 26:1 (1977), 8  crossref
    4. B.N. Allison, “Models of isotropic simple Lie algebras”, Communications in Algebra, 7:17 (1979), 1835  crossref
    5. S. M. Skryabin, “Sharp estimnew series of simple Lie algebras of characteristic 3”, Russian Acad. Sci. Sb. Math., 76:2 (1993), 389–406  mathnet  crossref  mathscinet  zmath  isi
    6. V. G. Kac, “Corrections to the paper of B. Yu. Weisfeller and V. G. Kac “Exponentials in Lie algebras of characteristic $p$””, Russian Acad. Sci. Izv. Math., 45:1 (1995), 229–229  mathnet  crossref  mathscinet  zmath  isi
    7. Gordon Brown, “Families of simple Lie algebras of characteristic two”, Communications in Algebra, 23:3 (1995), 941  crossref
    8. Yu. B. Ermolaev, “On the proportionality of Lie words in classical Lie algebras”, Russian Math. (Iz. VUZ), 46:9 (2002), 23–34  mathnet  mathscinet  zmath  elib
    9. Sofiane Bouarroudj, Pavel Grozman, Dimitry Leites, “Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix”, SIGMA, 5 (2009), 060, 63 pp.  mathnet  crossref  mathscinet
    10. S. Bouarroudj, A. V. Lebedev, F. Vagemann, “Deformations of the Lie Algebra $\mathfrak{o}(5)$ in Characteristics $3$ and $2$”, Math. Notes, 89:6 (2011), 777–791  mathnet  crossref  crossref  mathscinet  isi
    11. M. I. Kuznetsov, O. A. Mulyar, “Maximal tori of the Frank algebra”, J. Math. Sci., 185:3 (2012), 440–447  mathnet  crossref
    12. Sh. Sh. Ibraev, “O tsentralnykh rasshireniyakh klassicheskikh algebr Li”, Sib. elektron. matem. izv., 10 (2013), 450–453  mathnet
    13. T.B.. Gregory, “Winter Map Inverses”, APM, 04:07 (2014), 303  crossref
    14. Kenji Iohara, Fabio Gavarini, “Singular Degenerations of Lie Supergroups of Type $D(2,1;a)$”, SIGMA, 14 (2018), 137, 36 pp.  mathnet  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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