arXiv:1012.2169 Abstract | arXiv Analytics

arXiv:1012.2169 [math.GR]Abstract References Reviews Resources

On the derivation algebra of the free Lie algebra and trace maps

Published 2010-12-10, updated 2011-02-16Version 3

We calculate the irreducible decomposition of the images of the Johnson homomorphisms of the automorphism group of a free group and a free metabelian group. We determine the abelianization of the derivation algebra of the Chen Lie algebra as a Lie algebra, and show that the abelianizaton is given by the degree one part and the Morita's trace maps. We also consider twisted cohomology groups of the automorphism group of a free nilpotent group. We show that the trace map for the exterior product defines a non-trivial twisted second cohomology class of it.

Comments: 40 pages. We add a link to our preprint in the reference [43]

Categories: math.GR, math.RT

Subjects: 20F28, 17B40, 20G05

Keywords: free lie algebra, derivation algebra, automorphism group, non-trivial twisted second cohomology class, chen lie algebra

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