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On the basis-conjugating automorphism groups of free groups and free metabelian groups
Published online by Cambridge University Press: 08 December 2014
Abstract
In this paper we study the images of the Johnson homomorphisms of the basis-conjugating automorphism groups of free groups and free metabelian groups. In particular, we show that the Johnson image is contained in a certain proper Lie subalgebra $\mathfrak{p}$Mn of the derivation algebra of the Chen Lie algebra. Furthermore, we completely determine the Johnson images, and give the abelianisation of
$\mathfrak{p}$Mn as a Lie algebra by using Morita's trace maps.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 158 , Issue 1 , January 2015 , pp. 83 - 109
- Copyright
- Copyright © Cambridge Philosophical Society 2014
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