On some structures of Lie algebroids on the cotangent bundles (Q6606757)

The authors construct Lie algebroid structures on the cotangent bundle \(T^*M\) of a manifold \(M\). Some basic notions of algebroids and Poisson geometry are first presented. The authors then recall that the tangent bundle \(TM\) of a manifold \(M\) is a well-known algebroid with the identity map as the anchor map and the standard commutator of vector fields as the bracket. It is also known that to any Poisson structure on \(M\), one can associate a canonical Lie algebroid on \(T^*M\). The main purpose of this work is to select vector fields to obtain new structures of Lie algebroids on \(T^*M\). Some examples are discussed in detail.\N\NFor the entire collection see [Zbl 1531.53004].