Reduction of Poisson–Nijenhuis Lie algebroids to symplectic-Nijenhuis Lie algebroids with a nondegenerate Nijenhuis tensor

Reduction of Symplectic Lie Algebroids by a Lie Subalgebroid and a Symmetry Lie Group⋆

We describe the reduction procedure for a symplectic Lie algebroid by a Lie subalgebroid and a symmetry Lie group. Moreover, given an invariant Hamiltonian function we obtain the corresponding reduced Hamiltonian dynamics. Several examples illustrate the generality of the theory.

Lie, symplectic and Poisson groupoids and their Lie algebroids

Lie Algebroids and Lie Pseudoalgebras

Lie algebroids and Lie pseudoalgebras arise from a wide variety of constructions in differential geometry; they have been introduced repeatedly into the geometry, physics and algebra literatures since the 1950s, under some 14 different terminologies. The first main part (Sections 2-5) of this survey describes the four principal classes of examples, emphazising that each arises by means of a gen...

Horizontal Subbundle on Lie Algebroids

Providing an appropriate definition of a horizontal subbundle of a Lie algebroid will lead to construction of a better framework on Lie algebriods. In this paper, we give a new and natural definition of a horizontal subbundle using the prolongation of a Lie algebroid and then we show that any linear connection on a Lie algebroid generates a horizontal subbundle and vice versa. The same correspo...

Invariants of Lie algebroids

Several new invariants of Lie algebroids have been discovered recently. We give an overview of these invariants and establish several relationships between them.