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Algebra Logika, 2007, Volume 46, Number 5, Pages 585–605 (Mi al316)  

This article is cited in 23 scientific papers (total in 23 papers)

$\delta$-Derivations of simple finite-dimensional Jordan superalgebras

I. B. Kaygorodov

Novosibirsk State University

Abstract: We describe non-trivial $\delta$-derivations of semisimple finite-dimensional Jordan algebras over an algebraically closed field of characteristic not 2, and of simple finite-dimensional Jordan superalgebras over an a gebraically closed field of characteristic 0. For these classes of algebras and superalgebras, non-zero $\delta$-derivations are shown to be missing for $\delta\ne0,1/2,1$, and we give a complete account of 1/2-derivations.

Keywords: $\delta$-derivation, simple finite-dimensional Jordan superalgebra.

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English version:
Algebra and Logic, 2007, 46:5, 318–329

Bibliographic databases:

UDC: 512.554
Received: 10.01.2007

Citation: I. B. Kaygorodov, “$\delta$-Derivations of simple finite-dimensional Jordan superalgebras”, Algebra Logika, 46:5 (2007), 585–605; Algebra and Logic, 46:5 (2007), 318–329

Citation in format AMSBIB
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\by I.~B.~Kaygorodov
\paper $\delta$-Derivations of simple finite-dimensional Jordan superalgebras
\jour Algebra Logika
\yr 2007
\vol 46
\issue 5
\pages 585--605
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\transl
\jour Algebra and Logic
\yr 2007
\vol 46
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\pages 318--329
\crossref{https://doi.org/10.1007/s10469-007-0032-0}
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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. I. B. Kaygorodov, “$\delta$-derivations of classical Lie superalgebras”, Siberian Math. J., 50:3 (2009), 434–449  mathnet  crossref  mathscinet  isi
    2. I. B. Kaigorodov, “$\delta$-Superderivations of simple finite-dimensional Jordan and Lie superalgebras”, Algebra and Logic, 49:2 (2010), 130–144  mathnet  crossref  mathscinet  zmath  isi
    3. Zusmanovich P., “On delta-derivations of Lie algebras and superalgebras”, J. Algebra, 324:12 (2010), 3470–3486  crossref  mathscinet  zmath  isi  elib  scopus
    4. Zhang Runxuan, Zhang Yongzheng, “Generalized derivations of Lie superalgebras”, Commun. Algebra, 38:10 (2010), 3737–3751  crossref  mathscinet  zmath  isi  elib  scopus
    5. I. B. Kaigorodov, “Ob obobschennom duble Kantora”, Vestn. SamGU. Estestvennonauchn. ser., 2010, no. 4(78), 42–50  mathnet
    6. V. N. Zhelyabin, I. B. Kaygorodov, “On $\delta$-superderivations of simple superalgebras of Jordan brackets”, St. Petersburg Math. J., 23:4 (2012), 665–677  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    7. I. B. Kaygorodov, “$(n+1)$-ary derivations of simple $n$-ary algebras”, Algebra and Logic, 50:5 (2011), 470–471  mathnet  crossref  mathscinet  zmath  isi
    8. I. Kaygorodov, “$\delta$-Superderivations of Semisimple Finite-Dimensional Jordan Superalgebras”, Math. Notes, 91:2 (2012), 187–197  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    9. A. I. Shestakov, “Ternary derivations of separable associative and Jordan algebras”, Siberian Math. J., 53:5 (2012), 943–956  mathnet  crossref  mathscinet  isi
    10. I. B. Kaygorodov, “On $\delta$-derivations of $n$-ary algebras”, Izv. Math., 76:6 (2012), 1150–1162  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. I. B. Kaygorodov, “$(n+1)$-ary derivations of simple $n$-ary Malcev algebras”, St. Petersburg Math. J., 25:4 (2014), 575–585  mathnet  crossref  mathscinet  zmath  isi  elib
    12. I. B. Kaigorodov, “Ob obobschennykh $\delta$-differentsirovaniyakh”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 9/1(110), 12–21  mathnet  zmath  elib
    13. I. B. Kaygorodov, “$(n+1)$-ary Derivations of Semisimple Filippov algebras”, Math. Notes, 96:2 (2014), 208–216  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    14. Kaygorodov I. Okhapkina E., “Delta-Derivations of Semisimple Finite-Dimensional Structurable Algebras”, J. Algebra. Appl., 13:4 (2014), 1350130  crossref  mathscinet  zmath  isi  elib  scopus
    15. I. B. Kaygorodov, Yu. S. Popov, “Alternative algebras admitting derivations with invertible values and invertible derivations”, Izv. Math., 78:5 (2014), 922–936  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. A. I. Shestakov, “Ternary derivations of Jordan superalgebras”, Algebra and Logic, 53:4 (2014), 323–348  mathnet  crossref  mathscinet  isi
    17. Kaygorodov I. Lopatin A. Popov Yu., “Conservative Algebras of 2-Dimensional Algebras”, Linear Alg. Appl., 486 (2015), 255–274  crossref  mathscinet  zmath  isi  elib  scopus
    18. Kaygorodov I. Popov Yu., “Generalized Derivations of (Color) N-Ary Algebras”, Linear Multilinear Algebra, 64:6 (2016), 1086–1106  crossref  mathscinet  zmath  isi  elib  scopus
    19. Kaygorodov I. Popov Yu., “a Characterization of Nilpotent Nonassociative Algebras By Invertible Leibniz-Derivations”, J. Algebra, 456 (2016), 323–347  crossref  mathscinet  zmath  isi  scopus
    20. Doosti A. Saeedi F. Tajnia S., “Some Properties of M-Isoclinism and Id-Derivations in Filippov Algebras”, Cogent Math., 4 (2017), 1309740  crossref  mathscinet  isi
    21. Kaygorodov I. Lopatin A. Popov Yu., “The Structure of Simple Noncommutative Jordan Superalgebras”, Mediterr. J. Math., 15:2 (2018), UNSP 33  crossref  mathscinet  isi
    22. Kaygorodov I. Lopatin A. Popov Yu., “Jordan Algebras Admitting Derivations With Invertible Values”, Commun. Algebr., 46:1 (2018), 69–81  crossref  mathscinet  zmath  isi  scopus
    23. Saeedi F., Sheikh-Mohseni S., “On Id-Derivations of Filippov Algebras”, Asian-Eur. J. Math., 11:4 (2018), 1850050  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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