Revista de la
Unión Matemática Argentina
Linear Poisson structures and Hom-Lie algebroids
Esmaeil Peyghan, Amir Baghban, and Esa Sharahi
Volume 60, no. 2 (2019), pp. 299–313

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Considering Hom-Lie algebroids in some special cases, we obtain some results of Lie algebroids for Hom-Lie algebroids. In particular, we introduce the local splitting theorem for Hom-Lie algebroids. Moreover, linear Hom-Poisson structure on the dual Hom-bundle will be introduced and a one-to-one correspondence between Hom-Poisson structures and Hom-Lie algebroids will be presented. Also, we introduce Hamiltonian vector fields by using linear Poisson structures and show that there exists a relation between these vector fields and the anchor map of a Hom-Lie algebroid.