Norio Iwase
Mailing Adress: Faculty of Mathematics, Kyushu University, Motooka 744, Fukuoka 819-0395, Japan
E-mail Adress: iwase_AT__AT_math.kyushu-u.ac.jp
Authors.
Akira Kono and myself
Journal.
Proc. Roy. Soc. Edinburgh. 129 (1999), 773-785.
Abstract.
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.
It was shown that there is a homotopy theoretic approach that proves the results of Kozima and the second author for any 1-connected finite loop spaces, at odd primes.
In this paper, we use the rationalisation of the classifying spaces 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 of G in BLG satisfies the homotopy commutativity for any non-homotopy commutative loop space G, where LG denotes the space of free loops on G.
- Adjoint action of a finite loop space II (adobe-pdf file, 203782 bytes)