Polynomials And The Mod 2 Steenrod Algebra
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| Author | : Grant Walker (Mathematician) |
| Publisher | : Cambridge University Press |
| Total Pages | : 381 |
| Release | : 2018 |
| Genre | : Polynomials |
| ISBN | : 1108414451 |
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.
| Author | : Grant Walker |
| Publisher | : Cambridge University Press |
| Total Pages | : 371 |
| Release | : 2018 |
| Genre | : Mathematics |
| ISBN | : 1108414486 |
The first of two volumes covering the Steenrod algebra and its various applications. Suitable as a graduate text.
| Author | : Grant Walker |
| Publisher | : Cambridge University Press |
| Total Pages | : 381 |
| Release | : 2017-11-09 |
| Genre | : Mathematics |
| ISBN | : 1108355927 |
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.
| Author | : Paolo Aluffi |
| Publisher | : Cambridge University Press |
| Total Pages | : 396 |
| Release | : 2022-04-07 |
| Genre | : Mathematics |
| ISBN | : 1108890547 |
Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the second of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.
| Author | : David Jordan |
| Publisher | : Cambridge University Press |
| Total Pages | : 407 |
| Release | : 2023-08-17 |
| Genre | : Mathematics |
| ISBN | : 1009097350 |
Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.
| Author | : Scott Balchin |
| Publisher | : Cambridge University Press |
| Total Pages | : 357 |
| Release | : 2021-11-18 |
| Genre | : Mathematics |
| ISBN | : 1108931944 |
A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.
| Author | : Alexander A. Ivanov |
| Publisher | : Cambridge University Press |
| Total Pages | : 584 |
| Release | : 2023-08-17 |
| Genre | : Mathematics |
| ISBN | : 1009338056 |
Covering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.
| Author | : Kelli Francis-Staite |
| Publisher | : Cambridge University Press |
| Total Pages | : 224 |
| Release | : 2023-12-31 |
| Genre | : Mathematics |
| ISBN | : 1009400207 |
Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C∞-schemes', which allow differential geometers to study a huge range of singular spaces, including 'infinitesimals' and infinite-dimensional spaces. These are applied in synthetic differential geometry, and derived differential geometry, the study of 'derived manifolds'. Differential geometers also study manifolds with corners. The cube is a 3-dimensional manifold with corners, with boundary the six square faces. This book introduces 'C∞-schemes with corners', singular spaces in differential geometry with good notions of boundary and corners. They can be used to define 'derived manifolds with corners' and 'derived orbifolds with corners'. These have applications to major areas of symplectic geometry involving moduli spaces of J-holomorphic curves. This work will be a welcome source of information and inspiration for graduate students and researchers working in differential or algebraic geometry.
| Author | : Paolo Aluffi |
| Publisher | : Cambridge University Press |
| Total Pages | : 417 |
| Release | : 2022-04-07 |
| Genre | : Mathematics |
| ISBN | : 1108792502 |
Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.
| Author | : Hamid Abban |
| Publisher | : Cambridge University Press |
| Total Pages | : 368 |
| Release | : 2022-09-30 |
| Genre | : Mathematics |
| ISBN | : 1009190822 |
Written in celebration of Miles Reid's 70th birthday, this illuminating volume contains 11 papers by leading mathematicians in and around algebraic geometry, broadly related to the themes and interests of Reid's varied career. Just as in Reid's own scientific output, some of the papers give comprehensive accounts of the state of the art of foundational matters, while others give expositions of subject areas or techniques in concrete terms. Reid has been one of the major expositors of algebraic geometry and a great influence on many in this field – this book hopes to inspire a new generation of graduate students and researchers in his tradition.
