IndecomposableA-module summands inH
*
V which are unstable algebras |
| |
Authors: | Hans-Werner Henn Lionel Schwartz |
| |
Institution: | 1. Mathematisches Institut der Universit?t, Im Neuenheimer Feld 288, D-6900, Heidelberg, Federal Republic of Germany 2. Université de Paris-Sud, Mathématiques, Batiment 425, UA 1169 du CNRS, F-91405, Orsay Cedex, France
|
| |
Abstract: | Letp be a prime and denote byA the modp Steenrod algebra. We determine the indecomposableA-module summands ofH*((ℤ/p))
d
;F
p
which admit the structure of an unstableA-algebra. In fact, it turns out that this is equivalent to the problem of determining those indecomposableA-module summands which arise as the modp cohomology of a space (or even a classifying space of a finite group). We reduce this problem to one in modular representation
theory, namely for whichd andp is the projective cover of the trivial one dimensional GL(d,F
p
) representationF
p
a permutation module. Our solution of this latter problem makes use of the classification of subgroups of GL(d,F
p
) acting transitively on (F
p
)
d
\{0} and hence depends on the classification of finite simple groups (on Feit-Thompson's odd order theorem ifp=2). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|