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Mat. Zametki, 2014, Volume 96, Issue 2, Pages 217–227 (Mi mz9382)  

This article is cited in 9 scientific papers (total in 9 papers)

$(n+1)$-ary Derivations of Semisimple Filippov algebras

I. B. Kaygorodovab

a Universidade de São Paulo, Instituto de Matemática e Estatística, Brazil
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: The structure of generalized and $(n+1)$-ary derivations of simple and semisimple finite-dimensional Filippov algebras over an algebraically closed field of characteristic zero is described. An example of a semisimple ternary Maltsev algebra is given which is not a Filippov algebra and admits a nontrivial $4$-ary derivation.

Keywords: $n+1$-ary derivation, semisimple Filippov algebra, simple finite-dimensional Filippov algebra, ternary Maltsev algebra.

DOI: https://doi.org/10.4213/mzm9382

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English version:
Mathematical Notes, 2014, 96:2, 208–216

Bibliographic databases:

UDC: 512.554
Received: 17.04.2012
Revised: 30.09.2013

Citation: I. B. Kaygorodov, “$(n+1)$-ary Derivations of Semisimple Filippov algebras”, Mat. Zametki, 96:2 (2014), 217–227; Math. Notes, 96:2 (2014), 208–216

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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, “Ob obobschennykh delta-differentsirovaniyakh”, Vestnik Samarskogo gosudarstvennogo universiteta, 2013, no. 9-1(110), 12–21  mathnet  zmath  elib
    2. I. Kaygorodov, E. Okhapkina, “$\delta$-derivations of semisimple finite-dimensional structurable algebras”, J. Algebra. Appl., 13:4 (2014), 1350130, 12 pp.  crossref  mathscinet  zmath  isi  scopus
    3. I. Kaygorodov, Yu. Popov, “Commentary to: Generalized derivations of Lie triple systems”, Open Math., 14 (2016), 543–544  crossref  mathscinet  zmath  isi  elib  scopus
    4. I. Kaygorodov, Yu. Popov, “A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations”, J. Algebra, 456 (2016), 323–347  crossref  mathscinet  zmath  isi  elib  scopus
    5. I. Kaygorodov, Yu. Popov, “Generalized derivations of (color) $n$-ary algebras”, Linear Multilinear Algebra, 64:6 (2016), 1086–1106  crossref  mathscinet  zmath  isi  elib  scopus
    6. I. Kaygorodov, Yu. Volkov, “Conservative algebras of 2-dimensional algebras, II”, Comm. Algebra, 45:8 (2017), 3413–3421  crossref  mathscinet  zmath  isi  scopus
    7. A. Doosti, F. Saeedi, S. Tajnia, “Some properties of $m$-isoclinism and $ ID^*$-derivations in Filippov algebras”, Cogent Math., 4 (2017), 1309740  crossref  mathscinet  isi
    8. F. Saeedi, S. Sheikh-Mohseni, “On $\mathrm{ID}^*$-derivations of Filippov algebras”, Asian-Eur. J. Math., 11:4 (2018), 1850050, 9 pp.  crossref  mathscinet  zmath  isi  scopus
    9. Beites P.D., Kaygorodov I., Popov Yu., “Generalized Derivations of Multiplicative N-Ary Hom- Color Algebras”, Bull. Malays. Math. Sci. Soc., 42:1 (2019), 315–335  crossref  mathscinet  zmath  isi  scopus
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