Classification of certain $ n $-Derivations of Hom-Lie superalgebras

Mukhtar Ahmad; Shakir Ali; Abu Zaid Ansari; Intan Muchtadi-Alamsyah; Faiza Shujat; Mukhtar Ahmad; Shakir Ali; Abu Zaid Ansari; Intan Muchtadi-Alamsyah; Faiza Shujat

doi:10.3934/math.2026884

AIMS Mathematics

2026, Volume 11, Issue 7: 21846-21884. doi: 10.3934/math.2026884

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Classification of certain $ n $-Derivations of Hom-Lie superalgebras

1.
Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha no. 10, Bandung 40132, Indonesia
2.
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
3.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia
4.
Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha no. 10, Bandung 40132, Indonesia
5.
Department of Mathematics, College of Science, Taibah University, Madinah, Saudi Arabia

Received: 04 April 2026 Revised: 06 July 2026 Accepted: 08 July 2026 Published: 23 July 2026
MSC : 15A99, 17B10, 17B67, 16G30

Let $ \chi $ be a Hom-Lie superalgebra and $ n\geq 2 $ be a fixed integer. In this paper, we study the Lie $ n $-derivation algebra $ hN\operatorname{Der}(\chi) $ as well as the generalized Lie $ n $-derivation algebra $ hGN\operatorname{Der}(\chi) $. We also analyze the structures of the $ n $-centroids, the $ n $-quasi centroids, and the central $ n $-derivations, and examine how they relate to $ hN\operatorname{Der}(\chi) $ and $ hGN\operatorname{Der}(\chi) $. Moreover, we obtain a full classification of $ n $-derivations of Hom-Lie superalgebras and demonstrate that, for simple Hom-Lie superalgebras, one has $ hN\operatorname{Der}(\chi) = h\operatorname{Der}(\chi) $.
- $ n $-derivation,
- Hom-Lie $ n $-derivation,
- superalgebra,
- Hom-Lie superalgebra,
- centroid,
- quasi centroid
Citation: Mukhtar Ahmad, Shakir Ali, Abu Zaid Ansari, Intan Muchtadi-Alamsyah, Faiza Shujat. Classification of certain $ n $-Derivations of Hom-Lie superalgebras[J]. AIMS Mathematics, 2026, 11(7): 21846-21884. doi: 10.3934/math.2026884

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Abstract

Let $ \chi $ be a Hom-Lie superalgebra and $ n\geq 2 $ be a fixed integer. In this paper, we study the Lie $ n $-derivation algebra $ hN\operatorname{Der}(\chi) $ as well as the generalized Lie $ n $-derivation algebra $ hGN\operatorname{Der}(\chi) $. We also analyze the structures of the $ n $-centroids, the $ n $-quasi centroids, and the central $ n $-derivations, and examine how they relate to $ hN\operatorname{Der}(\chi) $ and $ hGN\operatorname{Der}(\chi) $. Moreover, we obtain a full classification of $ n $-derivations of Hom-Lie superalgebras and demonstrate that, for simple Hom-Lie superalgebras, one has $ hN\operatorname{Der}(\chi) = h\operatorname{Der}(\chi) $.

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