Defines Hom-Poisson-Nijenhuis structures on Hom-Lie algebroids and Hom-Dirac structures on Hom-Courant algebroids, showing they obey analogous properties to non-Hom versions including a hierarchy, Maurer-Cartan relation, and a bijection with Poisson structures plus isomorphisms on M.
On Poisson quasi-Nijenhuis Lie algebroids
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abstract
We propose a definition of Poisson quasi-Nijenhuis Lie algebroids as a natural generalization of Poisson quasi-Nijenhuis manifolds and show that any such Lie algebroid has an associated quasi-Lie bialgebroid. Therefore, also an associated Courant algebroid is obtained. We introduce the notion of a morphism of quasi-Lie bialgebroids and of the induced Courant algebroids morphism and provide some examples of Courant algebroid morphisms. Finally, we use paired operators to deform doubles of Lie and quasi-Lie bialgebroids and find an application to generalized complex geometry.
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math.SG 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Hom-Poisson-Nijenhuis structures on Hom-Lie algebroids and Hom-Dirac structures on Hom-Courant algebroids
Defines Hom-Poisson-Nijenhuis structures on Hom-Lie algebroids and Hom-Dirac structures on Hom-Courant algebroids, showing they obey analogous properties to non-Hom versions including a hierarchy, Maurer-Cartan relation, and a bijection with Poisson structures plus isomorphisms on M.