Transposed $\delta$-Poisson algebra structures on null-filiform associative algebras

TL;DR

This paper classifies transposed $ abla$-Poisson algebra structures on null-filiform associative algebras, revealing their characterization by polynomial roots and showing that all $ abla$-Poisson structures are trivial.

Contribution

It provides a complete classification of transposed $ abla$-Poisson algebras on null-filiform associative algebras and demonstrates that all such structures are trivial.

Findings

Algebras characterized by roots of $ abla^3 - 3 abla^2 + 2 abla$

Complete classification for each $ abla$ value

All $ abla$-Poisson structures are trivial

Abstract

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