Work

n-Derivations of Lie Superalgebras: Structure, Decomposition, and Central Extensions

Year: 2026

Type: article

Abstract: Let n≥2 be fixed, and let Λ be a Lie superalgebra over a commutative ring R. We investigate the structure of the algebra Dern(Λ) of n-derivations. We show that Dern(Λ) is a Z2-graded Lie superalgebra and that its elements preserve n-perfect graded ideals, thereby inducing n-derivations on the corresponding quotients. We obtain a direct-sum decomposition with explicit cross terms and describe n-derivations of split central extensions, including the contributions from maps into the n-center. For perfect centerless Lie superalgebras that are (n−1)-torsion-free, we prove that every n-derivation is an ordinary derivation; consequently, all n-derivations are inner when all ordinary derivations are inner. We also exhibit solvable examples for which Der(Λ) is properly contained in Dern(Λ). These results clarify the roles of the grading, ideals, centers, and split central extensions in the theory of n-derivations.

Source: Axioms

DOI: 10.3390/axioms15110794

Authors: Abu Zaid Ansari, Mukhtar Ahmad, Majed Albaity, Faiza Shujat

Institutions: Islamic University of Madinah, Bandung Institute of Technology, King Abdulaziz University, Taibah University

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

OpenAlex ID: W7223904978

FWCI:

Cites: 22

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Related to: 10