Nonabelian omni-Lie algebroids

Abstract

In this paper, we study the structure of nonabelian omni-Lie algebroids. Firstly, taking Lie algebroid (E,[\cdot ,\cdot {]}_E, {\rho }_E) as the starting point, a nonabelian omni-Lie algebroid is defined on direct sum bundle \mathfrak{D} E⨁\mathfrak{J}E, where \mathfrak{D} E and \mathfrak{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.

Key words： Nonabelian omni-Lie algebroid; omni-Lie algebroid; trivial deformation; matched pair of Leibniz algebroids

Acknowlegements

The research was supported by the National Natural Science Foundation of China (Grant Nos. 11961049, 11601219).

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