@article{Bi2024, 
author = {Yanhui Bi and Zhixiong Chen and Zhuo Chen and Maosong Xiang},
title = {The geometric constraints on Filippov algebroids},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {11007-11023},
keywords = {Filippov algebroids, anchored bundles, Filippov connections, Bianchi-Filippov identity, Nambu-Poisson structures},
url = {https://www.sciopen.com/article/10.3934/math.2024539},
doi = {10.3934/math.2024539},
abstract = {Filippov    n-algebroids are introduced by Grabowski and Marmo as a natural generalization of Lie algebroids. On this note, we characterized Filippov    n-algebroid structures by considering certain multi-input connections, which we called Filippov connections, on the underlying vector bundle. Through this approach, we could express the    n-ary bracket of any Filippov    n-algebroid using a torsion-free type formula. Additionally, we transformed the generalized Jacobi identity of the Filippov    n-algebroid into the Bianchi-Filippov identity. Furthermore, in the case of rank    n vector bundles, we provided a characterization of linear Nambu-Poisson structures using Filippov connections.}
}