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

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

2006-10-30

arxiv.org/abs/math/0610946v2

Geom. Topol. Monogr. 13 (2008) 147-168

Mathematics

Group Theory

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

Scientific paper

10.2140/gtm.2008.13.147

Let F_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

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