Tripolar Complex Fuzzy Lie Subalgebras of Lie Algebras

Authors

  • M. Balamurugan Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology
  • G. Ellammal Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology
  • Aiyared Iampan Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand https://orcid.org/0000-0002-0475-3320

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6489

Keywords:

Lie algebra, Tripolar complex fuzzy set, Tripolar complex fuzzy Lie subalgebra, Tripolar complex fuzzy Lie ideal, Nilpotent, Solvable

Abstract

The tripolar complex fuzzy set ($\mathcal{TCFS}$) is an extension of the bipolar complex fuzzy set ($\mathcal{BCFS}$), which itself generalizes traditional fuzzy sets and bipolar fuzzy sets. In this paper, we further develop this framework by introducing the concept of tripolar complex fuzzy Lie brackets and investigating their algebraic properties. Additionally, we demonstrate that the scalar multiplication and addition of tripolar complex fuzzy Lie subalgebras yield another tripolar complex fuzzy Lie subalgebra. Moreover, we establish that the homomorphic image of a nilpotent (or solvable) tripolar complex fuzzy Lie ideal remains a nilpotent (or solvable) tripolar complex fuzzy Lie ideal. Finally, we establish that every nilpotent tripolar complex fuzzy Lie ideal is solvable.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Algebra

License

Copyright (c) 2025 M. Balamurugan, G. Ellammal, Aiyared Iampan

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How to Cite

Tripolar Complex Fuzzy Lie Subalgebras of Lie Algebras. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6489. https://doi.org/10.29020/nybg.ejpam.v18i3.6489