Adjoint action of a finite loop space
Adjoint action of a finite loop space
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有限循环空间的伴随作用
DOI：
10.1090/s0002-9939-97-03924-5
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
Norio Iwase
中科院分区：
文献类型：
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作者：
Norio Iwase
Kozima和第二作者在一系列关于单李群及其上同调的分类研究的基础上，研究了紧单连通李群的伴随作用。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一个同伦理论方法来证明Kozima和第二作者的结果。在本文中，我们利用分类空间的合理化计算了假设无扭转的分类空间在素数2处的伴随作用和上同调。并且，通过使用Browder关于同伦可交换Hopf空间的kudoo - araki运算Q1的工作，我们证明了一般1连通有限环空间在素数2处的逆命题。这是因为包含j: G→BΛG满足任何非同伦可交换环空间G的同伦可交换性。
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 1connected finite loop spaces. In this paper, we use the rationalisation 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 → BΛG satisfies the homotopy commutativity for any non-homotopy commutative loop space G.