Nonabelian omni-Lie algebroids

Yanhui BI; Hongtao FAN; Danlu CHEN

doi:10.1007/s11464-022-1033-y

Front. Math. China ›› 2022, Vol. 17 ›› Issue (6) : 1037 -1049. DOI: 10.1007/s11464-022-1033-y

RESEARCH ARTICLE

Nonabelian omni-Lie algebroids

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Abstract

In this paper, we study the structure of nonabelian omni-Lie algebroids. Firstly, taking Lie algebroid $(E, [⋅, ⋅] E, ρ E)$ as the starting point, a nonabelian omni-Lie algebroid is defined on direct sum bundle $D E ⨁ J E$ , where $D E$ and $J E$ are, respectively, the gauge Lie algebroid and the jet bundle of vector bundle $E$ , and study its properties. Furthermore, it is concluded that the nonabelian omni-Lie algebroid is a trivial deformation of the omni-Lie algebroid, and the nonabelian omni-Lie algebroid is a matched pair of Leibniz algebroids.

Keywords

Nonabelian omni-Lie algebroid / omni-Lie algebroid / trivial deformation / matched pair of Leibniz algebroids

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Yanhui BI, Hongtao FAN, Danlu CHEN. Nonabelian omni-Lie algebroids. Front. Math. China, 2022, 17(6): 1037-1049 DOI:10.1007/s11464-022-1033-y

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