Polynomials and the mod 2 Steenrod Algebra: Volume 2, Representations of GL (n,F2)
Nonfiction, Science & Nature, Mathematics, Topology, Algebra
| Author: | Grant Walker, Reginald M. W. Wood | ISBN: | 9781108355926 |
| Publisher: | Cambridge University Press | Publication: | November 9, 2017 |
| Imprint: | Cambridge University Press | Language: | English |
| Author: | Grant Walker, Reginald M. W. Wood |
| ISBN: | 9781108355926 |
| Publisher: | Cambridge University Press |
| Publication: | November 9, 2017 |
| Imprint: | Cambridge University Press |
| Language: | English |
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.
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.
