阿贝尔hom-李环扩张的自同构  

AUTOMORPHISMS OF ABELIAN HOM-LIE RING EXTENSION

作　　者：徐晓宁[1,2] 赖燕 XU Xiao-ning;LAI Yan(School of Mathematics,Liaoning University,Shenyang 110036,China;Senior High School of Xinyang Dabieshan,Xinyang 464000,China)

机构地区：[1]辽宁大学数学院,辽宁沈阳110036 [2]信阳大别山高级中学,河南信阳464000

出　　处：《数学杂志》2020年第6期683-698,共16页Journal of Mathematics

基　　金：国家自然科学基金资助(11501274);辽宁省教育厅基金资助(L2015203).

摘　　要：本文研究了阿贝尔hom-李环扩张的自同构.利用阿贝尔扩张及中心扩张构造了三个正合序列,这些序列与群扩张的Wells序列相类似.利用这三个正合序列建立了自同构与群上同调之间的联系.其次研究了正合序列可分裂的条件.最后对我们的构造进行了相关应用.In this paper,the automorphisms of abelian hom-Lie ring extension are studied.Taking advantage of abelian extension and central extension,three exact sequences are contructed.The sequences were similar to Wells exact sequence for group extensions.The automorphisms are associated with group cohomology by using the three exact sequences.Then the conditions of the exact sequences splitting are discussed.Finally an application of our construction is given.

关 键 词：hom-李环 二阶上同调群 扩张 正合序列 

分 类 号：O152.5[理学—数学]