Polynomials and the mod 2 Steenrod Algebra
2 Paperback Volume Set
Part of London Mathematical Society Lecture Note Series
 Authors:
 Grant Walker, University of Manchester
 Reginald M. W. Wood, University of Manchester
 Date Published: November 2017
 availability: In stock
 format: Multiple copy pack
 isbn: 9781108414067
Multiple copy pack
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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 graduatelevel textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
Read more Algebraic and combinatorial treatment of Steenrod algebra
 Accessible to those without a background in topology
 Largely selfcontained with detailed proofs
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×Product details
 Date Published: November 2017
 format: Multiple copy pack
 isbn: 9781108414067
 dimensions: 227 x 152 x 43 mm
 weight: 1.12kg
 contains: 1 b/w illus.
 availability: In stock
Table of Contents
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 2dominance 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 A2module
20. The algebraic group Ḡ(n)
21. Endomorphisms of P(n) over A2
22. The Steinberg summands of P(n)
23. The dspike 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 4variable hit problem, I
30. The 4variable hit problem, II
Bibliography
Index of Notation for Volume 2
Index for Volume 2
Index of Notation for Volume 1
Index for Volume 1.
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