Del 441 - London Mathematical Society Lecture Note Series

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

Häftad, Engelska, 2017

AvGrant Walker,Reginald M. W. Wood,Grant (University of Manchester) Walker,Reginald M. W. (University of Manchester) Wood

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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.

Produktinformation

Utgivningsdatum2017-11-09
Mått151 x 227 x 22 mm
Vikt560 g
FormatHäftad
SpråkEngelska
SerieDel 441 i London Mathematical Society Lecture Note Series
Antal sidor370
FörlagCambridge University Press
ISBN9781108414487

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Topologi inom Naturvetenskap och teknik

Preface; 1. Steenrod squares and the hit problem; 2. Conjugate Steenrod squares; 3. The Steenrod algebra A2; 4. Products and conjugation in A2; 5. Combinatorial structures; 6. The cohit module Q(n); 7. Bounds for dim Qd(n); 8. Special blocks and a basis for Q(3); 9. The dual of the hit problem; 10. K(3) and Q(3) as F2GL(3)-modules; 11. The dual of the Steenrod algebra; 12. Further structure of A2; 13. Stripping and nilpotence in A2; 14. The 2-dominance theorem; 15. Invariants and the hit problem; Bibliography; Index of Notation for Volume 1; Index for Volume 1; Index of Notation for Volume 2; Index for Volume 2.