Grant Walker,
Grant (University of Manchester) Walker,
Reginald M. W. Wood,
Reginald M. W. (University of Manchester) Wood
e.a.
Polynomials and the mod 2 Steenrod Algebra: Volume 1, The Peterson Hit Problem
Paperback Engels 2017 9781108414487Levertijd ongeveer 9 werkdagen
Gratis verzonden
Samenvatting
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.
Specificaties
ISBN13:9781108414487
Taal:Engels
Bindwijze:Paperback
Aantal pagina's:370
Uitgever:Cambridge University Press
Serie:London Mathematical
Lezersrecensies
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Inhoudsopgave
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.
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