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

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.

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

References in corpus (2)

• Cohomological Aspects of Magnus Expansions
• On the Automorphism Tower of Free Nilpotent Groups

Cited by in corpus (8)

• Generating the Johnson filtration
• New series in the Johnson cokernels of the mapping class groups of surfaces
• Automorphisms of free groups, I
• A comparison of classes in the Johnson cokernels of the mapping class groups of surfaces
• On the structures of the Johnson cokernels of the basis-conjugating automorphism groups of free groups
• On the low dimensional cohomology groups of the IA-automorphism group of a free group of rank three
• On the graded quotients of the $\mathrm{SL}(m,\C)$-representation algebras of groups
• Meta-nilpotent knot invariants and symplectic automorphism groups of free nilpotent groups