aspg-21-3416-1791475513 20261008160513 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 25 4 Nader Mahmoud Taffach Faculty of Science, Department of Mathematics, Idlib University, Syria Mohammad Alsheikh Faculty of Science, Department of Mathematics, Idlib University, Syria Ahmed Hatip Gaziantep University, Department of Mathematics, Gaziantep, Turkey This paper introduces a novel approach to the concept of neutrosophic Lie algebra by leveraging the AH isometry framework. We establish foundational properties of neutrosophic Lie algebra, demonstrating that each neutrosophic algebra inherently fulfills the criteria of a Lie algebra. Moreover, we introduce distinct neutrosophic Lie algebraic structures, providing illustrative examples to support these constructs. By integrating neutrosophic logic, our approach effectively addresses indeterminacy, ambiguity, and imprecision, enhancing the classical algebraic structures with new dimensions of flexibility. The potential applications of neutrosophic Lie algebra are vast, particularly in fields requiring nuanced treatments of uncertainty. 2025 01 09 3416 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.250401 https://www.americaspg.com/journal/21/article/3416 https://www.americaspg.com/storage/11735271126.pdf