The geometric constraints on Filippov algebroids

Autor:	Bi, Yanhui, Chen, Zhixiong, Chen, Zhuo, Xiang, Maosong
Rok vydání:	2023
Předmět:	Mathematics - Rings and Algebras Mathematics - Differential Geometry 53C15 57R22
Zdroj:	AIMS Mathematics, 2024, 9(5):11007-11023
Druh dokumentu:	Working Paper
DOI:	10.3934/math.2024539
Popis:	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. Comment: 14pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.04180 Zobrazit plný text záznamu View this record from Arxiv