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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 1

Deformation of Kupershmidt operators and Kupershmidt-Nijenhuis structures of a Malcev algebra

Sami Mabrouk(University of Gafsa)0000-0003-2610-3262
Pages
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Publication Date
2022-02-14
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Finally, we establish a deformation theory of Kupershmidt operators in consistence with the general principles of deformation theories and introduce the notion of Nijenhuis elements.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The aim of this paper is to study infinitesimal deformations of a Malcev algebra with a representation and introduce the notion of Nijenhuis pair, which gives a trivial deformation of a Malcev algebra with a representation.
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Key Findings & Data:We introduce the notion of Kupershmidt-(dual-)Nijenhuis structure on a Malcev algebra with a representation.
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Conclusion & Impact:Finally, we establish a deformation theory of Kupershmidt operators in consistence with the general principles of deformation theories and introduce the notion of Nijenhuis elements.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:altenative algebras · Malcev algebras · representations

Abstract

The aim of this paper is to study infinitesimal deformations of a Malcev algebra with a representation and introduce the notion of Nijenhuis pair, which gives a trivial deformation of a Malcev algebra with a representation. We introduce the notion of Kupershmidt-(dual-)Nijenhuis structure on a Malcev algebra with a representation. Furthermore, we show that a Kupershmidt-(dual-)Nijenhuis structure gives rise to a hierarchy of Kupershmidt operators. Finally, we establish a deformation theory of Kupershmidt operators in consistence with the general principles of deformation theories and introduce the notion of Nijenhuis elements.

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Cite This Article

Mabrouk, S. (2022). Deformation of Kupershmidt operators and Kupershmidt-Nijenhuis structures of a Malcev algebra. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 1. https://doi.org/10.15672/hujms.923905

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