Representation up to homotopy of hom-Lie algebroids

Merati, S.; Farhangdoost, M. R.

doi:10.1142/s0219887818500743

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2019

2023

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Cited by 6 publications

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“…A Hom-Lie algebroid has its own geometric meaning and interesting examples, and it is more than a formal generalization of a Lie algebroid. Recently, many researchers have been interested in studying the algebraic and geometric concepts on Lie algebroids and Hom-Lie algebroids ( [3,5,7,8,10,11,12,13,14,15,16]).…”

Section: Introductionmentioning

confidence: 99%

Linear Poisson structures and Hom-Lie algebroids

Peyghan¹,

Baghban²

2019

Rev. Un. Mat. Argentina

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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.

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