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

Nonfiction, Science & Nature, Mathematics, Topology, Algebra
Cover of the book Polynomials and the mod 2 Steenrod Algebra: Volume 1, The Peterson Hit Problem by Grant Walker, Reginald M. W. Wood, Cambridge University Press
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Author: Grant Walker, Reginald M. W. Wood ISBN: 9781108355933
Publisher: Cambridge University Press Publication: November 9, 2017
Imprint: Cambridge University Press Language: English
Author: Grant Walker, Reginald M. W. Wood
ISBN: 9781108355933
Publisher: Cambridge University Press
Publication: November 9, 2017
Imprint: Cambridge University Press
Language: English

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.

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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.

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