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Algebra Logika, 2010, Volume 49, Number 2, Pages 195–215 (Mi al436)  

This article is cited in 20 scientific papers (total in 20 papers)

$\delta$-Superderivations of simple finite-dimensional Jordan and Lie superalgebras

I. B. Kaigorodovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: We introduce the concept of a $\delta$-superderivation of a superalgebra. $\delta$-Derivations of Cartan-type Lie superalgebras are treated, as well as $\delta$-superderivations of simple finite-dimensional Lie superalgebras and Jordan superalgebras over an algebraically closed field of characteristic 0. We give a complete description of $\frac12$-derivations for Cartan-type Lie superalgebras. It is proved that nontrivial $\delta$-(super)derivations are missing on the given classes of superalgebras, and as a consequence, $\delta$-superderivations are shown to be trivial on simple finite-dimensional noncommutative Jordan superalgebras of degree at least 2 over an algebraically closed field of characteristic 0. Also we consider $\delta$-derivations of unital flexible and semisimple finite-dimensional Jordan algebras over a field of characteristic not 2.

Keywords: $\delta$-superderivation, Cartan-type Lie superalgebra, simple finite-dimensional Lie superalgebra, Jordan superalgebra.

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English version:
Algebra and Logic, 2010, 49:2, 130–144

Bibliographic databases:

UDC: 512.554
Received: 23.09.2009

Citation: I. B. Kaigorodov, “$\delta$-Superderivations of simple finite-dimensional Jordan and Lie superalgebras”, Algebra Logika, 49:2 (2010), 195–215; Algebra and Logic, 49:2 (2010), 130–144

Citation in format AMSBIB
\by I.~B.~Kaigorodov
\paper $\delta$-Superderivations of simple finite-dimensional Jordan and Lie superalgebras
\jour Algebra Logika
\yr 2010
\vol 49
\issue 2
\pages 195--215
\jour Algebra and Logic
\yr 2010
\vol 49
\issue 2
\pages 130--144

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    This publication is cited in the following articles:
    1. I. B. Kaigorodov, “Ob obobschennom duble Kantora”, Vestn. SamGU. Estestvennonauchn. ser., 2010, no. 4(78), 42–50  mathnet
    2. 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
    3. 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
    4. I. Kaygorodov, “$\delta$-Superderivations of Semisimple Finite-Dimensional Jordan Superalgebras”, Math. Notes, 91:2 (2012), 187–197  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. A. I. Shestakov, “Ternary derivations of separable associative and Jordan algebras”, Siberian Math. J., 53:5 (2012), 943–956  mathnet  crossref  mathscinet  isi
    6. 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
    7. 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
    8. I. B. Kaigorodov, “Ob obobschennykh $\delta$-differentsirovaniyakh”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 9/1(110), 12–21  mathnet  zmath  elib
    9. 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
    10. 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
    11. 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
    12. A. I. Shestakov, “Ternary derivations of Jordan superalgebras”, Algebra and Logic, 53:4 (2014), 323–348  mathnet  crossref  mathscinet  isi
    13. A. Aboubakr, S. González, “Generalized reverse derivations on semiprime rings”, Siberian Math. J., 56:2 (2015), 199–205  mathnet  crossref  mathscinet  isi  elib  elib
    14. 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
    15. 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
    16. 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
    17. 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
    18. Kaygorodov I., Lopatin A., Popov Yu., “The Structure of Simple Noncommutative Jordan Superalgebras”, Mediterr. J. Math., 15:2 (2018), UNSP 33  crossref  mathscinet  isi
    19. Huang N., Chen L., Wang Ya., “Hom-Jordan Algebras and Their (K)-(a,B,C)-Derivations”, Commun. Algebr., 46:6 (2018), 2600–2614  crossref  mathscinet  zmath  isi  scopus
    20. 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
  • Алгебра и логика Algebra and Logic
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