This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's `hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n, F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
ISBN: | 9781108414456 |
Publication date: | 9th November 2017 |
Author: | Grant University of Manchester Walker, Reginald M W University of Manchester Wood |
Publisher: | Cambridge University Press |
Format: | Paperback |
Pagination: | 378 pages |
Series: | London Mathematical Society Lecture Note Series |
Genres: |
Topology |