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The equivariant Steenrod algebra. (English) Zbl 0675.55010
This paper presents a generalization of the mod p Steenrod algebra $$A^*$$ to G-equivariant cohomology theory for a finite group G. The coefficient ring is an arbitrary minimal Mackey functor field $${\mathcal F}$$. The equivariant Steenrod algebra graded on the real representation ring RO(G) is then defined as H$${\mathcal F}^*H{\mathcal F}$$, where H$${\mathcal F}$$ denotes the Eilenberg-MacLane G-spectrum associated to $${\mathcal F}$$. It is shown that the computation of H$${\mathcal F}^*H{\mathcal F}$$ reduces to $$HF^*HF$$, where F is some Galois extension of the finite field $${\mathbb{Z}}/p$$. To complete the computation, a description of the bimodule and Hopf algebra structures on $$HF^*HF$$ in terms of the structures on $$A^*$$ and Hom(F,F) is given.
Reviewer: D.Davis

##### MSC:
 55S10 Steenrod algebra 55M35 Finite groups of transformations in algebraic topology (including Smith theory) 55N25 Homology with local coefficients, equivariant cohomology 55N10 Singular homology and cohomology theory 55P42 Stable homotopy theory, spectra
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