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.