自由李代数的导子代数代数与迹映射
On the derivation algebra of the free Lie algebra and trace maps
摘要：
本文计算了自由群和自由亚交换群的自同构群的Johnson同态的象的不可约分解。本文确定了Chen李代数的导子代数代数为李代数的Abelianization，并证明了该Abelianization是由度1部分和Morita迹映射给出的.我们还考虑了自由幂零群的自同构群的扭上同调群。我们证明了外积的迹映射定义了它的一个非平凡的扭曲的第二上同调类。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
