Polynomials and the mod 2 Steenrod Algebra 2 Paperback Volume Set
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Format
Multiple copy pack
Språk
Engelska
Antal sidor
700
Utgivningsdatum
2017-11-09
Förlag
Cambridge University Press
Medarbetare
Wood, Reginald M. W.
Illustrationer
1 b/w illus.
Volymtitel
Polynomials and the mod 2 Steenrod Algebra 2 Paperback Volume Set
Dimensioner
234 x 164 x 43 mm
Vikt
1111 g
Antal komponenter
2
Komponenter
Paperback (2)
ISSN
0076-0552
ISBN
9781108414067
Polynomials and the mod 2 Steenrod Algebra 2 Paperback Volume Set

Polynomials and the mod 2 Steenrod Algebra 2 Paperback Volume Set

The Peterson Hit Problem / Representations of Gl(n,f2)

Multiple copy pack Engelska, 2017-11-09
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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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Övrig information

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.

Innehållsförteckning

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.