Adjoint action of a finite loop space. II

Norio Iwase, Akira Kono

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    1 Citation (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)773-785
    Number of pages13
    JournalRoyal Society of Edinburgh - Proceedings A
    Issue number4
    Publication statusPublished - 1999

    All Science Journal Classification (ASJC) codes

    • Mathematics(all)


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