I. B. Kaygorodov, “On $\delta$-derivations of $n$-ary algebras”, Izv. Math., 76:6 (2012), 1150

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Izvestiya: Mathematics, 2012, Volume 76, Issue 6, Pages 1150–1162
DOI: https://doi.org/10.1070/IM2012v076n06ABEH002618 (Mi im7907)

This article is cited in 16 scientific papers (total in 16 papers)

On

δ

$\delta$ -derivations of

n

$n$ -ary algebras

I. B. Kaygorodov^abc

^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

English version PDF (273 kB) Citations (16) Russian version article

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DOI: https://doi.org/10.1070/IM2012v076n06ABEH002618

Abstract: We give a description of

δ

$\delta$ -derivations of

(n + 1)

$(n+1)$ -dimensional

n

$n$ -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

δ

$\delta$ -derivations of Filippov algebras and show that there are no non-trivial

δ

$\delta$ -derivations of the simple ternary Mal'tsev algebra

M_{8}

$M_8$ .

Keywords:

δ

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

Received: 23.08.2011

Bibliographic databases:

Document Type: Article

UDC: 512.554

MSC: 17A36, 17A40, 17A42

Language: English

Original paper language: Russian

Citation: I. B. Kaygorodov, “On

δ

$\delta$ -derivations of

n

$n$ -ary algebras”, Izv. Math., 76:6 (2012), 1150–1162

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/im7907

https://doi.org/10.1070/IM2012v076n06ABEH002618

https://www.mathnet.ru/eng/im/v76/i6/p81

This publication is cited in the following 16 articles:

Jiang Yaxi, Kang Chuangchuang, Jiafeng Lü, “Classification of transposed Poisson 3-Lie algebras of dimension 3”, Communications in Algebra, 2025, 1
Abror Khudoyberdiyev, Bakhtiyor Yusupov, “Local and 2-Local $\frac{1}{2}$ -Derivations on Finite-Dimensional Lie Algebras”, Results Math, 79:5 (2024)
Zixin Zeng, Jiancai Sun, Honglian Zhang, “Transposed Poisson structures on Virasoro-type (super)algebras”, Journal of Geometry and Physics, 206 (2024), 105295
Nejib Saadaoui, Sergei Silvestrov, Springer Proceedings in Mathematics & Statistics, 426, Non-commutative and Non-associative Algebra and Analysis Structures, 2023, 761
Mabrouk S. Ncib O. Silvestrov S., “Generalized Derivations and Rota-Baxter Operators of N-Ary Hom-Nambu Superalgebras”, Adv. Appl. Clifford Algebr., 31:3 (2021), 32
Ferreira Bruno Leonardo Macedo, Kaygorodov I., Lopatkin V., “1/2-Derivations of Lie Algebras and Transposed Poisson Algebras”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 115:3 (2021), 142
Ibrahima Bakayoko, Sergei Silvestrov, Springer Proceedings in Mathematics & Statistics, 317, Algebraic Structures and Applications, 2020, 159
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
Ben Hassine A., Mabrouk S., Ncib O., “Some Constructions of Multiplicative N-Ary Hom-Nambu Algebras”, Adv. Appl. Clifford Algebr., 29:5 (2019), UNSP 88
Saeedi F., Sheikh-Mohseni S., “On Id-Derivations of Filippov Algebras”, Asian-Eur. J. Math., 11:4 (2018), 1850050
A. Ben Abdeljelil, M. Elhamdadi, A. Makhlouf, “Derivations of ternary Lie algebras and generalizations”, Int. Electron. J. Algebra, 21 (2017), 55–75
I. Kaygorodov, Yu. Popov, “Generalized derivations of (color) $n$ -ary algebras”, Linear and Multilinear Algebra, 2016
I. Kaygorodov, E. Okhapkina, “ $\delta$ -Derivations of semisimple finite-dimensional structurable algebras”, J. Algebra Appl., 13:4 (2014), 1350130, 12 pp.
I. B. Kaygorodov, “ $(n+1)$ -ary Derivations of Semisimple Filippov algebras”, Math. Notes, 96:2 (2014), 208–216
I. B. Kaygorodov, “ $(n+1)$ -ary derivations of simple $n$ -ary Malcev algebras”, St. Petersburg Math. J., 25:4 (2014), 575–585
I. B. Kaigorodov, “Ob obobschennykh $\delta$ -differentsirovaniyakh”, Vestn. SamGU. Estestvennonauchn. ser., 2013, no. 9/1(110), 12–21

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	687
Russian version PDF:	198
English version PDF:	40
References:	104
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