On the derivation algebra of the free Lie algebra and trace maps
Group Theory
2014-10-01 v3 Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1012.2169,
title = {On the derivation algebra of the free Lie algebra and trace maps},
author = {Naoya Enomoto and Takao Satoh},
journal= {arXiv preprint arXiv:1012.2169},
year = {2014}
}
Comments
40 pages. We add a link to our preprint in the reference [43]