Adjoint action of a finite loop space. II

Norio Iwase, Akira Kono

研究成果: Contribution to journalArticle査読

1 被引用数 (Scopus)

抄録

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 → BΛG satisfies the homotopy commutativity for any non-homotopy commutative loop space G.

本文言語英語
ページ(範囲)773-785
ページ数13
ジャーナルRoyal Society of Edinburgh - Proceedings A
129
4
DOI
出版ステータス出版済み - 1999

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

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