International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3416 2020 2020 Faculty of Science, Department of Mathematics, Idlib University, Syria admin admin Faculty of Science, Department of Mathematics, Idlib University, Syria Mohammad Alsheikh Gaziantep University, Department of Mathematics, Gaziantep, Turkey Ahmed Hatip 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 2025 01 09 10.54216/IJNS.250401 https://www.americaspg.com/articleinfo/21/show/3416