scholarly journals Cohomology mod $p$ of the $4$-connective fibre space of the classifying space of classical Lie groups

1984 ◽  
Vol 60 (2) ◽  
pp. 63-65
Author(s):  
Masana Harada ◽  
Akira Kono
Keyword(s):  
Lie Groups ◽  
Classifying Space ◽  
Fibre Space ◽  
Mod P

scholarly journals {${\rm Mod}\ p$} decomposition of compact Lie groups

1977 ◽  
Vol 13 (3) ◽  
pp. 627-680 ◽  
Author(s):  
Mamoru Mimura ◽  
Goro Nishida ◽  
Hirosi Toda
Keyword(s):  
Lie Groups ◽  
Compact Lie Groups ◽  
Mod P

scholarly journals Mod $p$ decompositions of non-simply connected Lie groups

2008 ◽  
Vol 48 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Daisuke Kishimoto ◽  
Akira Kono
Keyword(s):  
Lie Groups ◽  
Simply Connected ◽  
Mod P

Adjoint action of a finite loop space. II

1999 ◽  
Vol 129 (4) ◽  
pp. 773-785
Author(s):  
Norio Iwase ◽  
Akira Kono
Keyword(s):  
Lie Groups ◽  
Loop Space ◽  
Adjoint Action ◽  
Theoretic Approach ◽  
Loop Spaces ◽  
Classifying Space ◽  
Simply Connected ◽  
Prime 2 ◽  
Finite Loop

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.

Mod p associative H-spaces of given rank

1980 ◽  
Vol 88 (1) ◽  
pp. 153-160 ◽  
Author(s):  
J. R. Hubbuck
Keyword(s):  
Topological Group ◽  
Finite Number ◽  
Lie Groups ◽  
Homotopy Type ◽  
Homotopy Types ◽  
Simply Connected ◽  
Connected Spaces ◽  
Mod P

1. Few mod 2 finite simply-connected spaces are known to support an H-structure. These examples arise from products of Lie groups and seven spheres. It has been shown in (12) and (14) that the space of a mod 2 finite H-space of given rank can belong to only a finite number of different homotopy types. The situation at odd primes is very different; many examples of mod p finite H-spaces are known, such as p-localized odd-dimensional spheres. Therefore there are infinitely many homotopy types of prescribed rank. If one insists that the mod pH-space has a strictly associative multiplication, or equivalently has the homotopy type of a topological group, the picture is less clear. Examples have been constructed which do not arise from Lie groups and spheres but there are strong restrictions on just what can occur by these techniques, see (5). There are only finitely many known examples in each rank. We establish that there can in fact only be a finite number of possible homotopy types for the spaces.

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