The Peterson hit problem
著者
書誌事項
The Peterson hit problem
（London Mathematical Society lecture note series, 441 . Polynomials and the mod 2 Steenrod algebra / Grant Walker,
Cambridge University Press, 2018
- : pbk
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注記
Set ISBN for "Polynomials and the mod 2 Steenrod algebra": 9781108414067
Includes bibliographical references (p. 325-336) and indexes
内容説明・目次
内容説明
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.
目次
- 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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