On n -Derivations and n -Homomorphisms in Perfect Lie Superalgebras

Shakir Ali (), Amal S. Alali, Mukhtar Ahmad and Md Shamim Akhter
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Shakir Ali: Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
Amal S. Alali: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Mukhtar Ahmad: Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
Md Shamim Akhter: Department of Computer Science & Engineering, Jamia Hamdard, New Delhi 110062, India

Mathematics, 2025, vol. 13, issue 20, 1-21

Abstract: Let n ≥ 2 be a fixed integer. The aim of this paper is to investigate the properties of n -derivations within the framework of perfect Lie superalgebras over a commutative ring R . The main result shows that if the base ring contains 1 n − 1 , and L is a perfect Lie superalgebra with a center equal to zero, then any n -derivation of L is necessarily a derivation. Additionally, every n -derivation of the derivation algebra D e r ( L ) is an inner derivation. Moreover, we extend the concept of n -homomorphisms to mappings between Lie superalgebras L and L ′ and prove that under specific assumptions, homomorphisms, anti-homomorphisms, and their combinations are all n -homomorphisms. Finally, we conclude our paper with some open problems.

Keywords: Lie algebra; superalgebra; perfect Lie superalgebra; n-derivation; n-homomorphism; enveloping Lie superalgebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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