Nonabelian omni-Lie algebroids  

作　　者：Yanhui BI Hongtao FAN Danlu CHEN 

机构地区：[1]School of Mathematics and Information Sciences,Nanchang Hangkong University,Nanchang,330063,China

出　　处：《Frontiers of Mathematics in China》2022年第6期1037-1049,共13页中国高等学校学术文摘·数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11961049,11601219).

摘　　要：In this paper,we study the structure of nonabelian omni-Lie algebroids.Firstly,taking Lie algebroid(E,[·,·]_(E,ρE))as the starting point,a nonabelian omni-Lie algebroid is defined on direct sum bundle DE⊕JE,where DE and JE 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.

关 键 词：Nonabelian omni-Lie algebroid omni-Lie algebroid trivial deformation matched pair of Leibniz algebroids 

分 类 号：O15[理学—数学]