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.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Illustrationen
Worked examples or Exercises; 1 Line drawings, black and white
Maße
Höhe: 234 mm
Breite: 164 mm
Dicke: 43 mm
Gewicht
ISBN-13
978-1-108-41406-7 (9781108414067)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Grant Walker was a senior lecturer in the School of Mathematics at the University of Manchester before his retirement in 2005. Reginald M. W. Wood was a Professor in the School of Mathematics at the University of Manchester before his retirement in 2005.
Autor*in
University of Manchester
University of Manchester
Volume 1: 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; Volume 2: Preface; 16. The action of GL(n) on flags; 17. Irreducible F2GL(n)-modules; 18. Idempotents and characters; 19. Splitting P(n) as an A2-module; 20. The algebraic group ?(n); 21. Endomorphisms of P(n) over A2; 22. The Steinberg summands of P(n); 23. The d-spike module J(n); 24. Partial flags and J(n); 25. The symmetric hit problem; 26. The dual of the symmetric hit problem; 27. The cyclic splitting of P(n); 28. The cyclic splitting of DP(n); 29. The 4-variable hit problem, I; 30. The 4-variable hit problem, II; Bibliography; Index of Notation for Volume 2; Index for Volume 2; Index of Notation for Volume 1; Index for Volume 1.
