Polynomials and the mod 2 Steenrod Algebra: Volume 1, The Peterson Hit Problem

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Polynomials and the mod 2 Steenrod Algebra: Volume 1, The Peterson Hit Problem is written by Grant Walker and published by Cambridge University Press. It's available with International Standard Book Number or ISBN identification 1108359299 (ISBN 10) and 9781108359290 (ISBN 13).

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.