Poisson cohomology of "book" Poisson structures

TL;DR

This paper calculates the Poisson cohomology for a specific linear Poisson structure associated with the 'book' Lie algebra, providing insights into its algebraic and geometric properties.

Contribution

It explicitly determines the Poisson cohomology groups for the 'book' Lie algebra's dual structure, a novel computation in this context.

Findings

Poisson cohomology groups are explicitly computed.

Results reveal the algebraic structure of the cohomology.

Insights into deformation and stability of the 'book' Poisson structure.

Abstract

We compute the Poisson cohomology of the linear Poisson structure dual to the n-dimensional "book" Lie algebra, defined by [e_0,e_i]=e_i, [e_i,e_j]=0, for i,j=1,...,n-1.