摘要
本文研究了非交换omni-李代数胚结构问题.首先,以李代数胚(E,[·,·]_E,ρ_E)为起点,在直和丛■上定义了非交换omni-李代数胚,其中■和■分别是向量丛E的规范李代数胚和jet丛,同时研究其性质.进一步,证明了非交换omni-李代数胚是omni-李代数胚的平凡形变,并且非交换omni-李代数胚是一个莱布尼茨代数胚的匹配对.
In this paper,we study the structure of nonabelian omni-Lie algebroids.First,taking Lie algebroid(E,[·,·]E,ρE)as the starting point,a nonabelian omni-Lie algebroid is defined on direct sum bundle■,where■and■are,respectively,the gauge Lie algebroid and the jet bundle of vector bundle E,and we 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.
作者
毕艳会
范宏涛
陈丹露
BI Yanhui;FAN Hongtao;CHEN Danlu(School of Mathematics and Information Sciences,Nanchang Hangkong University,Nanchang,Jiangxi,330063,P.R.China)
出处
《数学进展》
CSCD
北大核心
2022年第5期879-890,共12页
Advances in Mathematics（China）
基金
国家自然科学基金(Nos.11961049,11601219)。
