Basis-conjugating automorphisms of a free group and associated Lie algebras

Abstract

Let F_n = <x_1,...,x_n> denote the free group with generators {x_1,...,x_n}. Nielsen and Magnus described generators for the kernel of the canonical epimorphism from the automorphism group of F_n to the general linear group over the integers. In particular among them are the automorphisms chi_{k,i} which conjugate the generator x_k by the generator x_i leaving the x_j fixed for j not k. A computation of the cohomology ring as well as the Lie algebra obtained from the descending central series of the group generated by chi_{k,i} for i<k is given here. Partial results are obtained for the group generated by all chi_{k,i}.

This is the version published by Geometry & Topology Monographs on 22 February 2008

References in corpus (4)

• Cohomological Aspects of Magnus Expansions
• The integral cohomology of the group of loops
• Centralizers of Lie Algebras Associated to the Descending Central Series of Certain Poly-Free Groups
• Stable homology of automorphism groups of free groups

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