Transposed Poisson Structures on the planar Galilean conformal algebra

TL;DR

This paper proves that all transposed Poisson structures on the planar Galilean conformal algebra are trivial by showing that every half-derivation is scalar, simplifying the algebra's structure.

Contribution

It establishes that all 2-derivations are scalar, leading to the conclusion that transposed Poisson structures are trivial on this algebra.

Findings

All 2-derivations are scalar.

All transposed Poisson structures are trivial.

Simplifies understanding of the algebra's structure.

Abstract

Each $\frac{1}{2}$-derivation of the planar Galilean conformal algebra is proven to be a scalar. As a corollary, all transposed Poisson structures on the planar Galilean conformal algebra are trivial.