Transposed Poisson structures on Witt-type algebras

TL;DR

This paper classifies all transposed Poisson structures on various Witt-type algebras by computing specific derivations and analyzing their algebraic properties.

Contribution

It provides a complete classification of transposed Poisson structures on deformative Schrödinger-Witt, Witt algebras, and Heisenberg-Witt algebras, expanding understanding of their algebraic structures.

Findings

Computed 1/2-derivations on key Witt-type algebras

Classified all transposed Poisson structures on these algebras

Extended algebraic understanding of non-finitely graded Witt and Heisenberg-Witt algebras

Abstract

We compute $\frac{1}{2}$-derivations on the deformative Schr\"{o}dinger-Witt algebra, on not-finitely graded Witt algebras $W_n(G)$, and on not-finitely graded Heisenberg-Witt algebra $HW_n(G)$. We classify all transposed Poisson structures on such algebras.