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Polynomials and the mod 2 Steenrod Algebra

Volume 1. The Peterson Hit Problem

Part of London Mathematical Society Lecture Note Series

  • Date Published: November 2017
  • availability: Available
  • format: Paperback
  • isbn: 9781108414487


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About the Authors
  • 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.

    • Algebraic and combinatorial treatment accessible to those without a background in topology
    • Largely self-contained with detailed proofs
    • Volume 1 is suitable for use as a graduate-level text
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    Product details

    • Date Published: November 2017
    • format: Paperback
    • isbn: 9781108414487
    • length: 370 pages
    • dimensions: 227 x 151 x 22 mm
    • weight: 0.56kg
    • availability: Available
  • Table of Contents

    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
    Index of Notation for Volume 1
    Index for Volume 1
    Index of Notation for Volume 2
    Index for Volume 2.

  • Authors

    Grant Walker, University of Manchester
    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, University of Manchester
    Reginald M. W. Wood was a Professor in the School of Mathematics at the University of Manchester before his retirement in 2005.

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