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Polynomials and the mod 2 Steenrod Algebra de Grant Walker

Polynomials and the mod 2 Steenrod Algebra

Autor Grant Walker, Reginald M. W. Wood
en Limba Engleză Paperback – 28 feb 2018
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.
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Specificații

ISBN-13: 9781108414456
ISBN-10: 1108414451
Pagini: 380
Ilustrații: 1 b/w illus.
Dimensiuni: 152 x 229 x 20 mm
Greutate: 0.55 kg
Editura: Cambridge University Press
Locul publicării:Cambridge, United Kingdom

Cuprins

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.

Recenzii

'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 Moreover, the material in Volume 2 using the cyclic splitting of P(n) is based in part upon the unpublished Ph.D. thesis of Helen Weaver … Much of the material covered has not hitherto appeared in book form, and these volumes should serve as a useful reference.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

Descriere

The second of two volumes covering the Steenrod algebra and its various applications. Ideal for researchers in pure mathematics.