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It is a generalization of the intuitionistic fuzzy set, giving the notion of neutral membership degrees along with the positive and negative ones. Lie groups and Lie algebras have become indispensable for a lot of fields in mathematical and intellectual physics. In 1872, Lie began his work in the field of continuous transformation groups, later named after him as Lie groups. These have become a fundamental body of interest in themselves. In this paper, the authors presented the notion of the picture fuzzy Lie algebra, picture fuzzy Lie sub-algebra, ideal, and homomorphism. 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