Deformation of the Poisson structure related to algebroid bracket of differential forms and application to real low dimentional Lie algebras (Q2418906)

This paper studies classification of some real low dimensional Lie algebras from the perspective of Poisson geometry and Lie algebroid formalisms. The Casimir functions are calculated. By vertically lifting of the Poisson vector fields from Poisson manifold to its tangent bundle, new Poisson tensors and classes of bi-Hamiltonian manifolds are obtained (this method is also known as deformations of Poisson structures using the bi-Hamiltonian structure). Application to a few examples of low dimensional Lie algebras yields new invariants. For example, by taking the three dimensional nilpotent Lie algebra \(A_{3,1}\), one could generate nilpotent Lie algebras of dimension six. For the entire collection see [Zbl 1408.53003].