Hyperstructures on Lie algebroids

Abstract

We define hypersymplectic structures on Lie algebroids recovering, as particular cases, all the classical results and examples of hypersymplectic structures on manifolds. We prove a 1-1 correspondence theorem between hypersymplectic structures and (pseudo-)hyperkähler structures. We show that the hypersymplectic framework is very rich in already known compatible pairs of tensors such as Poisson-Nijenhuis, $\Omega N$ and $P\Omega$ structures.

References in corpus (2)

• Courant algebroids, derived brackets and even symplectic supermanifolds
• Quasi-Lie bialgebroids and twisted Poisson manifolds

Cited by in corpus (1)

• Hypersymplectic structures with torsion on Lie algebroids