Transposed Poisson Structures on Low Dimensional Quasi-Filiform Lie Algebras of Maximum Length

The article first computes $$\frac{1}{2}$$ -derivations of five and six dimensional quasi-filiform Lie algebras of maximum length. Then, it constructs non-trivial transposed Poisson algebras using these $$\frac{1}{2}$$ -derivations of quasi-filiform Lie algebras of maximum length. We have also established commutative associative multiplication to build a transposed Poisson algebra associated with a given Lie algebra.

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