arXiv Analytics

Sign in

arXiv:0903.4997 [math.AT]AbstractReferencesReviewsResources

An algebraic introduction to the Steenrod algebra

Larry Smith

Published 2009-03-28Version 1

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.

Comments: This is the version published by Geometry & Topology Monographs on 14 November 2007
Journal: Geom. Topol. Monogr. 11 (2007) 327-348
Categories: math.AT
Subjects: 55S10, 13A50
Related articles: Most relevant | Search more
arXiv:1104.3613 [math.AT] (Published 2011-04-19)
On the anti-automorphism of the Steenrod algebra: II
arXiv:2106.10630 [math.AT] (Published 2021-06-20)
A note on the hit problem for the Steenrod algebra in some generic degrees
arXiv:2305.19250 [math.AT] (Published 2023-05-30)
The Steenrod algebra is self-injective, and the Steenrod algebra is not self-injective

Links

Toolbox