Transposed Poisson structures on solvable Lie algebras with filiform nilradical

TL;DR

This paper explores the construction of transposed Poisson algebras on solvable Lie algebras with a specific nilradical, using 1/2-derivations to establish compatible associative multiplications.

Contribution

It introduces a method to construct transposed Poisson structures on solvable Lie algebras via 1/2-derivations, expanding understanding of algebraic structures with nilradicals.

Findings

Described 1/2-derivations of solvable Lie algebras with filiform nilradical

Constructed nontrivial transposed Poisson algebras using these derivations

Established a link between Lie algebra derivations and associative multiplications

Abstract

In this article, we described 1/2-derivations of solvable Lie algebras with a thread-like nilradical. Nontrivial transposed Poisson algebras with solvable Lie algebras are constructed. That is, by using 1/2-derivations of Lie algebras, we have established commutative associative multiplication to construct a transposed Poisson algebra with an associated given Lie algebra.