Polynomials and the mod 2 Steenrod Algebra
Polynomials and the mod 2 Steenrod Algebra
$99.99
USDThis 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 of Steenrod algebra
- Accessible to those without a background in topology
- Largely self-contained with detailed proofs
Reviews & endorsements
'In these volumes, the authors draw upon the work of many researchers in addition to their own work, in places presenting new proofs or improvements of results. Moreover, the material in Volume 2 using the cyclic splitting of P(n) is based in part upon the unpublished Ph.D. thesis of Helen Weaver … Much of the material covered has not hitherto appeared in book form, and these volumes should serve as a useful reference. … readers will find different aspects appealing.' Geoffrey M. L. Powell, Mathematical Reviews
Product details
November 2017Adobe eBook Reader
9781108359283
0 pages
1 b/w illus.
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- 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.
