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Polynomial Invariant Rings Isomorphic as Modules Over the Steenrod Algebra
Author(s) -
Segal Joel
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700001666
Subject(s) - steenrod algebra , mathematics , cohomology , pure mathematics , invariant (physics) , homotopy , algebra over a field , pointwise , mathematical analysis , mathematical physics
The paper is concerned with rings of polynomial invariants of finite groups. In particular, it will be shown that these rings are isomorphic as modules over the Steenrod algebra P* if and only if the group representations are pointwise conjugate . An application to cohomology is the construction of classifying spaces of finite groups which are not homotopy equivalent, but where the cohomology rings are isomorphic as unstable modules over the (topological) Steenrod algebra.