Adjoint action of a finite loop space. II
Adjoint action of a finite loop space. II
复制标题
有限循环空间的伴随作用。
DOI：
10.1017/s0308210500013135
复制
发表时间：
1999
期刊：
影响因子：
--
通讯作者：
A. Kono
中科院分区：
文献类型：
--
作者：
Norio Iwase;A. Kono
紧单连通李群的伴随作用由小岛和第二作者在单李群的分类及其上同调的一系列研究的基础上进行了研究。在奇素数下，第一作者证明了对于任意1-连通有限环空间，存在同伦理论方法证明了小岛和第二作者的结果。本文利用分类空间的有理化，在素数2上计算了假设自由挠率的分类空间的伴随作用和上同调，并利用Browder关于同伦交换Hopf空间Kudo-Araki运算Q1的工作，给出了一般1-连通有限环空间在素数2上的逆运算.这是因为包含j：G&g；Bag满足任意非同伦交换环路空间G的同伦交换性.
Adjoint actions of compact simply connected Lie groups are studied by Kozima and the second author based on the series of studies on the classification of simple Lie groups and their cohomologies. At odd primes, the first author showed that there is a homotopy theoretic approach that will prove the results of Kozima and the second author for any 1-connected finite loop spaces. In this paper, we use the rationalization of the classifying space to compute the adjoint actions and the cohomology of classifying spaces assuming torsion free hypothesis, at the prime 2. And, by using Browder's work on the Kudo–Araki operations Q1 for homotopy commutative Hopf spaces, we show the converse for general 1-connected finite loop spaces, at the prime 2. This can be done because the inclusion j: G > BAG satisfies the homotopy commutativity for any non-homotopy commutative loop space G.