Transposed $δ$-Poisson algebra structures on null-filiform associative algebras

In this paper, we consider transposed $δ$-Poisson algebras, which are a generalization of transposed $δ$-Poisson algebras. In particular, we describe all transposed $δ$-Poisson algebras of associative null-filiform algebras. It can be seen that these algebras are characterized by the roots of the polynomial δ³ - 3δ² + 2δ. A complete classification of transposed $δ$-Poisson algebras corresponding to each value of the parameter $δ$ is provided. Furthermore, we construct all $δ$-Poisson algebra structures on null-filiform associative algebras, and show that they are trivial $δ$-Poisson algebras.