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ISSN (electronic): 1464-8997
ISSN (print): 1464-8989

An algebraic introduction to the Steenrod algebra

Larry Smith

Geometry & Topology Monographs 11 (2007) 327–348

DOI: 10.2140/gtm.2007.11.327

arXiv: 0903.4997

Abstract

The purpose of these notes is to provide an introduction to the Steenrod algebra in an algebraic manner avoiding any use of cohomology operations. The Steenrod algebra is presented as a subalgebra of the algebra of endomorphisms of a functor. The functor in question assigns to a vector space over a Galois field the algebra of polynomial functions on that vector space: the subalgebra of the endomorphisms of this functor that turns out to be the Steenrod algebra if the ground field is the prime field, is generated by the homogeneous components of a variant of the Frobenius map.

Keywords

Steenrod algebra, Frobenius map, invariant theory

Mathematical Subject Classification

Primary: 55S10

Secondary: 13A50

References
Publication

Received: 9 March 2005
Accepted: 20 June 2005
Published: 14 November 2007

Authors
Larry Smith
AG-Invariantentheorie
Mittelweg 3
D 37133 Friedland
Federal Republic of Germany