Basis-conjugating automorphisms of a free group and associated Lie algebras
Abstract
Let Fn = <x1,...,xn> denote the free group with generators x1,...,xn. Nielsen and Magnus described generators for the kernel of the canonical epimorphism from the automorphism group of Fn to the general linear group over the integers. In particular among them are the automorphisms chik,i which conjugate the generator xk by the generator xi leaving the xj 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 chik,i for i<k is given here. Partial results are obtained for the group generated by all chik,i.
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