General

With roots in the nineteenth century, Lie theory has since found many and varied applications in mathematics and mathematical physics, to the point where it is now regarded as a classical branch of mathematics in its own right. This graduate text focuses...

This book deals with automorphism groups of compact Riemann surfaces, of genus at least two, viewed as factor groups of Fuchsian groups. The author uses modern methods from computational group theory and representation theory, providing classifications...

This book comprises a collection of papers from participants at the IMCS Workshop on Computational and Geometric Aspects of Modern Algebra, held at Heriot-Watt University in 1998. Written by leading researchers, the papers cover a wide range of topics in...

Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an important research topic for algebraic geometers and coding theorists. The focus in this application of algebraic...

Tilting theory originates in the representation theory of finite dimensional algebras. Today the subject is of much interest in various areas of mathematics, such as finite and algebraic group theory, commutative and non-commutative algebraic geometry,...

The focus of this book is the study of the noncommutative aspects of rings and modules, and the style will make it accessible to anyone with a background in basic abstract algebra. Features of interest include an early introduction of projective and...

This volume reflects the fruitful connections between group theory and topology. It contains articles on cohomology, representation theory, geometric and combinatorial group theory. Some of the world's best known figures in this very active area of...

This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and...

The focus of this book is the study of the noncommutative aspects of rings and modules, and the style will make it accessible to anyone with a background in basic abstract algebra. Features of interest include an early introduction of projective and...

The Atlas of Finite Groups by J. H. Conway, R. A. Parker, S. P. Norton and the editors of this book, was published in 1985, and has proved itself to be an indispensable tool to all researchers in group theory and many related areas. The present book is...

Finite fields are algebraic structures in which there is much research interest and they have been shown to have a wide range of applications. These proceedings give a state-of-the-art account of the area of finite fields and their applications in...

The invention of ideals by Dedekind in the 1870s was well ahead of its time, and proved to be the genesis of what today we would call algebraic number theory. His memoir 'Sur la Theorie des Nombres Entiers Algebriques' first appeared in instalments in...

There has been a resurgence of interest in classical invariant theory driven by several factors: new theoretical developments; a revival of computational methods coupled with powerful new computer algebra packages; and a wealth of new applications,...

This 2003 book is concerned with two fundamental problems in low-dimensional topology. Firstly, the D(2)-problem, which asks whether cohomology detects dimension, and secondly the realization problem, which asks whether every algebraic 2-complex is...

This second volume of the two-volume book contains selected papers from the international conference 'Groups St Andrews 2001 in Oxford' which was held at the University of Oxford in August 2001. Five main lecture courses were given at the conference, and...

This first volume of the two-volume book contains selected papers from the international conference 'Groups St Andrews 2001 in Oxford' which was held at the University of Oxford in August 2001. Five main lecture courses were given at the conference, and...

Presented here are papers from the 1993 Como meeting on groups of Lie type and their geometries. The meeting was attended by many leading figures, as well as younger researchers in this area, and this book brings together many of their excellent...

In 1963 Walter Feit and John G. Thompson published a proof of a 1911 conjecture by Burnside that every finite group of odd order is solvable. This proof, which ran for 255 pages, was a tour-de-force of mathematics and inspired intense effort to classify...

This a comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry, in particular their relations with Poisson geometry and general connection theory. It covers much work done since the...

The articles in these two volumes arose from papers given at the 1991 International Symposium on Geometric Group Theory, and they represent some of the latest thinking in this area. Many of the world's leading figures in this field attended the...

The articles in these two volumes arose from papers given at the 1991 International Symposium on Geometric Group Theory, and they represent some of the latest thinking in this area. This first volume contains contributions from many of the world's...

Prior to the International Congress of 1990 in Japan, a workshop on algebra was held which included some of the best known figures in this field. Many of the expository surveys given at this workshop by distinguished mathematicians are included here...

This book is devoted to the theory of group representations, a young and promising area of modern algebra. It provides a detailed exposition of several central topics in the field, leading to the most current advances and developments. Much of the...

Sporadic Groups is the first step in a programme to provide a uniform, self-contained treatment of the foundational material on the sporadic finite simple groups. The classification of the finite simple groups is one of the premier achievements of modern...

Since the classification of finite simple groups was announced in 1980 the subject has continued to expand opening many new areas of research. This volume contains a collection of papers, both survey and research, arising from the 1990 Durham conference...

These volumes contain selected papers presented at the international conference on group theory held in St Andrews in 1989. The themes of the conference were combinatorial and computational group theory; four leading group theorists (J. A. Green, N. D...

The study of permutation groups has always been closely associated with that of highly symmetric structures. The objects considered here are countably infinite, but have only finitely many different substructures of any given finite size. They are...

The interaction between ergodic theory and discrete groups has a long history and much work was done in this area by Hedlund, Hopf and Myrberg in the 1930s. There has been a great resurgence of interest in the field, due in large measure to the...

This is the first of two volumes which will provide an introduction to modern developments in the representation theory of finite groups and associative algebras. The subject is viewed from the perspective of homological algebra and the theory of...

This book provides an introduction to the field of linear algebraic monoids. This subject represents a synthesis of ideas from the theory of algebraic groups, algebraic geometry, matrix theory and abstract semigroup theory. Since every representation of...

This book provides a striking synthesis of the standard theory of connections in principal bundles and the Lie theory of Lie groupoids. The concept of Lie groupoid is a little-known formulation of the concept of principal bundle and corresponding to the...

This book is concerned with subgroups of groups of the form GL(n,D) for some division ring D. In it the authors bring together many of the advances in the theory of skew linear groups. Some aspects of skew linear groups are similar to those for linear...

This book contains selected papers from the international conference Groups - St Andrews 1985. Five leading group theorists - Bachmuth, Baumslag, Neuman, Roseblade and Tits - have presented survey articles based on short lecture courses given at the...

This textbook is an introduction to the concept of factorization and its application to problems in algebra and number theory. With the minimum of prerequisites, the reader is introduced to the notion of rings, fields, prime elements and unique...

This book's aim is to make accessible techniques for studying Whitehead groups of finite groups, as well as a variety of related topics such as induction theory and p-adic logarithms. The author has included a lengthy introduction to set the scene for...

Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowledge of...

The unifying theme of this collection of papers by the very creative Russian mathematician I. M. Gelfand and his co-workers is the representation theory of groups and lattices. Two of the papers were inspired by application to theoretical physics; the...

The first half of the book is a general study of homomorphisms to simple artinian rings; the techniques developed here should be of interest to many algebraists. The second half is a more detailed study of special types of skew fields which have arisen...

This is the first book on the subject of FPF rings and the systematic use of the notion of the generator of the category mod-R of all right R-modules and its relationship to faithful modules. This carries out the program, explicit of inherent, in the...

Problem solving is an art that is central to understanding and ability in mathematics. With this series of books the authors have provided a selection of problems with complete solutions and test papers designed to be used with or instead of standard...