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Izv. RAN. Ser. Mat., 2012, Volume 76, Issue 6, Pages 81–94 (Mi izv7907)  

This article is cited in 8 scientific papers (total in 8 papers)

On $\delta$-derivations of $n$-ary algebras

I. B. Kaygorodovabc

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

Abstract: We give a description of $\delta$-derivations of $(n+1)$-dimensional $n$-ary Filippov algebras and, as a consequence, of simple finite-dimensional Filippov algebras over an algebraically closed field of characteristic zero. We also give new examples of non-trivial $\delta$-derivations of Filippov algebras and show that there are no non-trivial $\delta$-derivations of the simple ternary Mal'tsev algebra $M_8$.

Keywords: $\delta$-derivation, Filippov algebra, ternary Mal'tsev algebra.

DOI: https://doi.org/10.4213/im7907

Full text: PDF file (510 kB)
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English version:
Izvestiya: Mathematics, 2012, 76:6, 1150–1162

Bibliographic databases:

UDC: 512.554
MSC: 17A36, 17A40, 17A42
Received: 23.08.2011

Citation: I. B. Kaygorodov, “On $\delta$-derivations of $n$-ary algebras”, Izv. RAN. Ser. Mat., 76:6 (2012), 81–94; Izv. Math., 76:6 (2012), 1150–1162

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. I. B. Kaigorodov, “Ob obobschennykh $\delta$-differentsirovaniyakh”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 9/1(110), 12–21  mathnet  zmath  elib
    3. 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
    4. 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
    5. I. Kaygorodov, Yu. Popov, “Generalized derivations of (color) $n$-ary algebras”, Linear and Multilinear Algebra, 2016  crossref  mathscinet  scopus
    6. A. Ben Abdeljelil, M. Elhamdadi, A. Makhlouf, “Derivations of ternary Lie algebras and generalizations”, Int. Electron. J. Algebra, 21 (2017), 55–75  crossref  mathscinet  zmath  isi
    7. Saeedi F., Sheikh-Mohseni S., “On Id-Derivations of Filippov Algebras”, Asian-Eur. J. Math., 11:4 (2018), 1850050  crossref  mathscinet  zmath  isi  scopus
    8. 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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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