Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2)

Nonfiction, Science & Nature, Mathematics, Topology, Algebra
Cover of the book Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2) by Grant Walker, Reginald M. W. Wood, Cambridge University Press
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Author: Grant Walker, Reginald M. W. Wood ISBN: 9781108355926
Publisher: Cambridge University Press Publication: November 9, 2017
Imprint: Cambridge University Press Language: English
Author: Grant Walker, Reginald M. W. Wood
ISBN: 9781108355926
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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