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

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

2010-12-10

arxiv.org/abs/1012.2169v3

Mathematics

Group Theory

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

Scientific paper

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.

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