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arXiv · math/0610946

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

F R Cohen·J Pakianathan·V V Vershinin·Jie Wu
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Abstract

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<k is given here. Partial results are obtained for the group generated by all chi_{k,i}.

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F R Cohen, J Pakianathan, V V Vershinin, Jie Wu. 2006-10-30. Basis-conjugating automorphisms of a free group and associated Lie algebras. https://doi.org/10.2140/gtm.2008.13.147

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