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Sibirsk. Mat. Zh., 2009, Volume 50, Number 3, Pages 547–565 (Mi smj1980)  

This article is cited in 21 scientific papers (total in 21 papers)

$\delta$-derivations of classical Lie superalgebras

I. B. Kaygorodov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We consider the $\delta$-derivations of classical Lie superalgebras and prove that these superalgebras admit nonzero $\delta$-derivations only when $\delta=0,\frac12,1$. The structure of $\frac12$-derivations for classical Lie superalgebras is completely determined.

Keywords: $\delta$-derivation, Lie superalgebra.

Full text: PDF file (392 kB)
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English version:
Siberian Mathematical Journal, 2009, 50:3, 434–449

Bibliographic databases:

UDC: 512.554
Received: 05.03.2008

Citation: I. B. Kaygorodov, “$\delta$-derivations of classical Lie superalgebras”, Sibirsk. Mat. Zh., 50:3 (2009), 547–565; Siberian Math. J., 50:3 (2009), 434–449

Citation in format AMSBIB
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\by I.~B.~Kaygorodov
\paper $\delta$-derivations of classical Lie superalgebras
\jour Sibirsk. Mat. Zh.
\yr 2009
\vol 50
\issue 3
\pages 547--565
\mathnet{http://mi.mathnet.ru/smj1980}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2555880}
\transl
\jour Siberian Math. J.
\yr 2009
\vol 50
\issue 3
\pages 434--449
\crossref{https://doi.org/10.1007/s11202-009-0049-9}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67650471765}


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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. Kaigorodov, “$\delta$-Superderivations of simple finite-dimensional Jordan and Lie superalgebras”, Algebra and Logic, 49:2 (2010), 130–144  mathnet  crossref  mathscinet  zmath  isi
    2. Zusmanovich P., “On $\delta$-derivations of Lie algebras and superalgebras”, J. Algebra, 324:12 (2010), 3470–3486  crossref  mathscinet  zmath  isi  elib  scopus
    3. Zhang Runxuan, Zhang Yongzheng, “Generalized derivations of Lie superalgebras”, Comm. Algebra, 38:10 (2010), 3737–3751  crossref  mathscinet  zmath  isi  elib  scopus
    4. I. B. Kaigorodov, “Ob obobschennom duble Kantora”, Vestn. SamGU. Estestvennonauchn. ser., 2010, no. 4(78), 42–50  mathnet
    5. 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
    6. 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
    7. I. Kaygorodov, “$\delta$-Superderivations of Semisimple Finite-Dimensional Jordan Superalgebras”, Math. Notes, 91:2 (2012), 187–197  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    8. A. I. Shestakov, “Ternary derivations of separable associative and Jordan algebras”, Siberian Math. J., 53:5 (2012), 943–956  mathnet  crossref  mathscinet  isi
    9. 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
    10. 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
    11. Zheng K., Zhang Y., “On (Alpha, Beta, Gamma)-Derivations of Lie Superalgebras”, Int. J. Geom. Methods Mod. Phys., 10:10 (2013), 1350050  crossref  mathscinet  zmath  isi  elib  scopus
    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. A. I. Shestakov, “Ternary derivations of Jordan superalgebras”, Algebra and Logic, 53:4 (2014), 323–348  mathnet  crossref  mathscinet  isi
    15. 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
    16. A. Aboubakr, S. González, “Generalized reverse derivations on semiprime rings”, Siberian Math. J., 56:2 (2015), 199–205  mathnet  crossref  mathscinet  isi  elib  elib
    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. Zusmanovich P., “Special and Exceptional Mock-Lie Algebras”, Linear Alg. Appl., 518 (2017), 79–96  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. 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
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