caa a22 4500 388109149 CHVBK 20180307125348.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500013135 doi S0308210500013135 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500013135 Adjoint action of a finite loop space. II [Elektronische Daten] 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. Copyright © Royal Society of Edinburgh 1999 Iwase Norio Graduate School of Mathematics, Kyushu University Ropponmatsu, Fukuoka 810, Japan Kono Akira Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606, Japan Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 773-785 0308-2105 129:4<773 1999 129 PRM https://doi.org/10.1017/S0308210500013135 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500013135 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Iwase Norio Graduate School of Mathematics, Kyushu University Ropponmatsu, Fukuoka 810, Japan NATIONALLICENCE 700 1- Kono Akira Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606, Japan NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 773-785 0308-2105 129:4<773 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge