%0 Journal Article %T Hypersymplectic structures with torsion on Lie algebroids %A P. Antunes %A J. M. Nunes da Costa %J Mathematics %D 2015 %I arXiv %X Hypersymplectic structures with torsion on Lie algebroids are investigated. We show that each hypersymplectic structure with torsion on a Lie algebroid determines three Nijenhuis morphisms. From a contravariant point of view, these structures are twisted Poisson structures. We prove the existence of a one-to-one correspondence between hypersymplectic structures with torsion and hyperk\"{a}hler structures with torsion. We show that given a Lie algebroid with a hypersymplectic structure with torsion, the deformation of the Lie algebroid structure by any of the transition morphisms does not affect the hypersymplectic structure with torsion. We also show that if a triplet of $2$-forms is a hypersymplectic structure with torsion on a Lie algebroid $A$, then the triplet of the inverse bivectors is a hypersymplectic structure with torsion for a certain Lie algebroid structure on the dual $A^*$, and conversely. Examples of hypersymplectic structures with torsion are included. %U http://arxiv.org/abs/1501.00887v1