Transposed $\hat{I}´$-Poisson algebra structures on null-filiform associative algebras

Abstract

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

arXiv admin note: substantial text overlap with arXiv:2503.06295