Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2)
Cambridge University Press (Verlag)
978-1-108-41445-6 (ISBN)
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.
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.
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 Ḡ(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.
| Erscheinungsdatum | 10.11.2017 |
|---|---|
| Reihe/Serie | London Mathematical Society Lecture Note Series |
| Zusatzinfo | Worked examples or Exercises; 1 Line drawings, black and white |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 152 x 227 mm |
| Gewicht | 550 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-108-41445-1 / 1108414451 |
| ISBN-13 | 978-1-108-41445-6 / 9781108414456 |
| Zustand | Neuware |
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