Basis-conjugating automorphisms of a free group and associated Lie algebras
Group Theory
2012-02-21 v2 Algebraic Topology
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}.
Keywords
Cite
@article{arxiv.math/0610946,
title = {Basis-conjugating automorphisms of a free group and associated Lie algebras},
author = {F R Cohen and J Pakianathan and V V Vershinin and Jie Wu},
journal= {arXiv preprint arXiv:math/0610946},
year = {2012}
}
Comments
This is the version published by Geometry & Topology Monographs on 22 February 2008