Chen Lie algebras
Chen Lie algebras
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陈烈代数
DOI：
10.1155/s1073792804132017
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发表时间：
2003
影响因子：
1
通讯作者：
Alexander I. Suciu
中科院分区：
文献类型：
--
作者：
S. Papadima;Alexander I. Suciu
群G的Chen群是G的最大亚交换商G/G″的下中心级数. Chen群的直和是一个分次李代数，括号由群换位子诱导。如果G是形式空间的基本群，我们通过证明G的有理Chen李代数同构于G的有理holonomy李代数模第二导子代数，给出了Sullivan的一个基本结果的类似.根据Massey的思想，我们指出了群G的亚历山大不变量与它的整合李代数之间的联系.作为应用，我们确定了几类几何定义的群的Chen李代数，包括类曲面群，S3中某些链补的基本群，S3中超平面排列的补的基本群.对于链接群，我们锐化Massey和Traldi的Murasugi猜想的解决方案。对于排列群，证明了有理陈李代数是组合决定的。
The Chen groups of a finitely presented group G are the lower central series quotients of its maximal metabelian quotient G/G″. The direct sum of the Chen groups is a graded Lie algebra, with bracket induced by the group commutator. If G is the fundamental group of a formal space, we give an analog of a basic result of Sullivan by showing that the rational Chen Lie algebra of G is isomorphic to the rational holonomy Lie algebra of G modulo the second derived subalgebra. Following an idea of Massey, we point out a connection between the Alexander invariant of a group G defined by commutator-relators and its integral holonomy Lie algebra. As an application, we determine the Chen Lie algebras of several classes of geometrically defined groups, including surface-like groups, fundamental groups of certain link complements in S 3 , and fundamental groups of complements of hyperplane arrangements in ℂ l . For link groups, we sharpen Massey and Traldi's solution of the Murasugi conjecture. For arrangement groups, we prove that the rational Chen Lie algebra is combinatorially determined.