关于Brunnian辫子群的相对李代数的基  

A Basis for the Relative Lie Algebra of Brunnian Braids

作　　者：何莉莹 李京艳[2] HE Liying;LI Jingyan(Shijiazhuang Beijun Primary School,Shijiazhuang 050000,China;School of Mathematical Science,Hebei Normal University,Shijiazhuang 050024,China)

机构地区：[1]石家庄市北郡小学,石家庄050000 [2]河北师范大学数学科学学院,石家庄050024

出　　处：《数学年刊（A辑）》2020年第4期449-464,共16页Chinese Annals of Mathematics

基　　金：国家自然科学基金资助项目(No.11201314,No.11302136);石家庄铁道大学研究生创新项目(No.YC201735)和石家庄铁道大学优青基金的资助。

摘　　要：Brunnian辫子群与球面上的同伦群关系密切.在本文中,研究了Brunnian辫子群相对于纯辫子群的相对李代数L^(P)(Brunn),通过其与Brunnian辫子群相对于自由群的相对李代数L^(Fn-1)(Brunn)的关系,并借助自由群的李代数L(F_(n-1))的Hall基给出相对李代数L^(P)(Brunn)的基.Brunnian braids have interesting relations with homotopy groups of spheres.In this paper,the authors investigate the Lie algebra of the descending central series related to subgroup of the pure group.In order to determine the basis for the relative Lie algebra L^(P)(Brunn),the authors study the relationship of L^(P)(Brunn)and L_(Fn-1)(Brunn).With the help of the Hall basis of free Lie algebra L_(Fn-1),the basis of relative Lie algebra L^(P)(Brunn)is given.

关 键 词：Brunnian辫子群 相对李代数 自由群 Hall基 

分 类 号：O152.4[理学—数学]