Galois Theories

Author: Francis Borceux,George Janelidze

Publisher: Cambridge University Press

ISBN: 9780521803090

Category: Mathematics

Page: 341

View: 726

DOWNLOAD NOW »

Develops Galois theory in a more general context, emphasizing category theory.
Release

Galois Theory, Hopf Algebras, and Semiabelian Categories

Author: George Janelidze

Publisher: American Mathematical Soc.

ISBN: 0821832905

Category: Mathematics

Page: 570

View: 2770

DOWNLOAD NOW »

This volume is based on talks given at the Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras, and Semiabelian Categories held at The Fields Institute for Research in Mathematical Sciences (Toronto, ON, Canada). The meeting brought together researchers working in these interrelated areas. This collection of survey and research papers gives an up-to-date account of the many current connections among Galois theories, Hopf algebras, and semiabelian categories. The book features articles by leading researchers on a wide range of themes, specifically, abstract Galois theory, Hopf algebras, and categorical structures, in particular quantum categories and higher-dimensional structures. Articles are suitable for graduate students and researchers, specifically those interested in Galois theory and Hopf algebras and their categorical unification.
Release

Galois Theory, Hopf Algebras, and Semiabelian Categories

Author: George Janelidze, Bodo Pareigis, and Walter Tholen

Publisher: American Mathematical Soc.

ISBN: 9780821871478

Category: Mathematics

Page: N.A

View: 2522

DOWNLOAD NOW »

Survey and research papers in this volume are based on talks given at a workshop held at The Fields Institute for Research in the Mathematical Sciences (Toronto, ON, Canada). It provides an up-to-date account by leading researchers on the many current connections among Galois theories, Hopf algebras, and semiabelian categories.
Release

Progress in Galois Theory

Proceedings of John Thompson's 70th Birthday Conference

Author: Helmut Voelklein,Tanush Shaska

Publisher: Springer Science & Business Media

ISBN: 0387235345

Category: Mathematics

Page: 168

View: 7703

DOWNLOAD NOW »

The legacy of Galois was the beginning of Galois theory as well as group theory. From this common origin, the development of group theory took its own course, which led to great advances in the latter half of the 20th cen tury. It was John Thompson who shaped finite group theory like no-one else, leading the way towards a major milestone of 20th century mathematics, the classification of finite simple groups. After the classification was announced around 1980, it was again J. Thomp son who led the way in exploring its implications for Galois theory. The first question is whether all simple groups occur as Galois groups over the rationals (and related fields), and secondly, how can this be used to show that all finite groups occur (the 'Inverse Problem of Galois Theory'). What are the implica tions for the stmcture and representations of the absolute Galois group of the rationals (and other fields)? Various other applications to algebra and number theory have been found, most prominently, to the theory of algebraic curves (e.g., the Guralnick-Thompson Conjecture on the Galois theory of covers of the Riemann sphere).
Release

Groups as Galois Groups

An Introduction

Author: Helmut Volklein

Publisher: Cambridge University Press

ISBN: 9780521562805

Category: Mathematics

Page: 248

View: 1314

DOWNLOAD NOW »

This book describes various approaches to the Inverse Galois Problem, a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory, algebraic geometry and number theory, topology, and analysis. Assuming only elementary algebra and complex analysis, the author develops the necessary background from topology, Riemann surface theory and number theory. The first part of the book is quite elementary, and leads up to the basic rigidity criteria for the realisation of groups as Galois groups. The second part presents more advanced topics, such as braid group action and moduli spaces for covers of the Riemann sphere, GAR- and GAL- realizations, and patching over complete valued fields. Graduate students and mathematicians from other areas (especially group theory) will find this an excellent introduction to a fascinating field.
Release

Galois Groups and Fundamental Groups

Author: Tamás Szamuely

Publisher: Cambridge University Press

ISBN: 0521888506

Category: Mathematics

Page: 270

View: 1028

DOWNLOAD NOW »

Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Release

Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras

Author: D. J. Benson

Publisher: Cambridge University Press

ISBN: 9780521636537

Category: Mathematics

Page: 260

View: 7747

DOWNLOAD NOW »

This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules. Thus, Dr. Benson's unique perspective in this book incorporates homological algebra and the theory of representations of finite-dimensional algebras. This volume is primarily concerned with the exposition of the necessary background material, and the heart of the discussion is a lengthy introduction to the (Auslander-Reiten) representation theory of finite dimensional algebras, in which the techniques of quivers with relations and almost-split sequences are discussed in some detail.
Release

Algebraic Number Theory

Author: A. Fröhlich,M. J. Taylor,Martin J. Taylor

Publisher: Cambridge University Press

ISBN: 9780521438346

Category: Mathematics

Page: 355

View: 7088

DOWNLOAD NOW »

This book provides a brisk, thorough treatment of the foundations of algebraic number theory on which it builds to introduce more advanced topics. Throughout, the authors emphasize the systematic development of techniques for the explicit calculation of the basic invariants such as rings of integers, class groups, and units, combining at each stage theory with explicit computations.
Release