An algebraic introduction to the Steenrod algebra

Details An algebraic introduction to the Steenrod algebra An algebraic introduction to the Steenrod algebra

2009-03-28

arxiv.org/abs/0903.4997v1

Geom. Topol. Monogr. 11 (2007) 327-348

Mathematics

Algebraic Topology

This is the version published by Geometry & Topology Monographs on 14 November 2007

Scientific paper

10.2140/gtm.2007.11.327

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.

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