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- Title
Chen Lie algebras.
- Authors
Papadima, Stefan; Suciu, Alexander I.
- Abstract
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 S3, and fundamental groups of complements of hyperplane arrangements in ℂℓ. 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.
- Subjects
FREE metabelian groups; LIE algebras; HOLONOMY groups; HYPERPLANES; COMMUTATORS (Operator theory)
- Publication
IMRN: International Mathematics Research Notices, 2004, Vol 2004, Issue 21, p1057
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1155/S1073792804132017