The equivariant Steenrod algebra
type: Item
instance of: scholarly article
title: The equivariant Steenrod algebra
zbMATH Open document ID: 0675.55010
DOI: 10.1016/0166-8641(89)90008-4
author: Melda Yaman Oruç
published in: Topology and its Applications
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 55S10
Mathematics Subject Classification ID: 55M35
Mathematics Subject Classification ID: 55N25
Mathematics Subject Classification ID: 55N10
Mathematics Subject Classification ID: 55P42
zbMATH DE Number: 4105866
zbMATH Keywords: equivariant cohomology theory
zbMATH Keywords: equivariant Steenrod algebra
MaRDI profile type: Publication
full work available at URL: 0166-8641(89)90008-4
OpenAlex ID: W2143707237
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description: scientific article; zbMATH DE number 4105866