何莉莹,李京艳.关于Brunnian辫子群的相对李代数的基[J].数学年刊A辑,2020,(4):449~464
关于Brunnian辫子群的相对李代数的基
A Basis for the Relative Lie Algebra of Brunnian Braids
Received:August 08, 2017  Revised:June 29, 2018
DOI:10.16205/j.cnki.cama.2020.0032
中文关键词:  Brunnian, 辫子群, 相对李代数, 自由群, Hall基
英文关键词:Brunnian braid, Relative Lie algebra, Free group, Hall basis
基金项目: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
Author NameAffiliation
HE Liying School of Mathematical Science, Hebei Normal University, Shijiazhuang 050024, China. 
LI Jingyan Corresponding author. Shijiazhuang Beijun Primary School, Shijiazhuang 050000, China. 
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中文摘要:
      \textrm{Brunnian辫子群与球面上的同伦群关系密切.在本文中, 研究了\textrm{Brunnian辫子群相对于纯辫子群的相对李代数L^{P}({\rm Brun}_{n}),通过其与\textrm{Brunnian辫子群相对于自由群的相对李代数L^{F_{n-1}}({\rm Brun}_{n})的关系,并借助自由群的李代数L(F_{n-1})的\textrm{Hall基给出相对李代数L^{P}({\rm Brun}_{n})的基.
英文摘要:
      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 LP(Brunn), the authors study the relationship of LP(Brunn) and LFnn-1(Brunn). With the help of the Hall basis of free Lie algebra L(Fn-1), the basis of relative Lie algebra LP (Brunn) is given.
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