Kategoria BISAC: Mathematics >> Group Theory

About the first edition:

"The text is geared to the needs of the beginning graduate student, covering with complete, well-written proofs the usual major branches of groups, rings, fields, and modules... n]one of the material one expects in a book like this is missing, and the level of detail is appropriate for its intended audience." (Alberto Delgado, MathSciNet)

"This text promotes the conceptual understanding of algebra as a whole, and that with great methodological mastery. Although the presentation is predominantly abstract...it nevertheless features a careful...

The aim of software engineering is to find methods for developing high quality software products at a reasonable cost. As more and more computers are being used in areas in which a malfunction of the system can be a source of serious losses or disturbances to the functioning of the society, the quality of software becomes a more and more critical factor of business success, human security, and safety. Examples of such application areas are enterprise management, public administration, and social insurance or post delivery services. The quality of services offered to the society depends on...

If F is a non-Archimedean local field, local class field theory can be viewed as giving a canonical bijection between the characters of the multiplicative group GL(1, F) of F and the characters of the Weil group of F. If n is a positive integer, the n-dimensional analogue of a character of the multiplicative group of F is an irreducible smooth representation of the general linear group GL(n, F). The local Langlands Conjecture for GL(n) postulates the existence of a canonical bijection between such objects and n-dimensional representations of the Weil group, generalizing class field...

Many group theorists all over the world have been trying in the last twenty-five years to extend and adapt the magnificent methods of the Theory of Finite Soluble Groups to the more ambitious universe of all finite groups. This is a natural progression after the classification of finite simple groups but the achievements in this area are scattered in various papers.

Our objectives in this book were to gather, order and examine all this material, including the latest advances made, give a new approach to some classic topics, shed light on some fundamental facts that still remain...

In the 1970's, James developped a characterictic-free'' approach to the representation theory of the symmetric group on n letters, where Specht modules and certain bilinear forms on them play a crucial role. In this framework, we obtain a natural parametrization of the irreducible representations, but it is a major open problem to find explicit formulae for their dimensions when the ground field has positive characteristic.

In a wider context, this problem is a special case of the problem of determining the irreducible representations of Iwahori--Hecke algebras at roots of...

One of the beautiful results in the representation theory of the finite groups is McKay's theorem on a correspondence between representations of the binary polyhedral group of SU(2) and vertices of an extended simply-laced Dynkin diagram.

The Coxeter transformation is the main tool in the proof of the McKay correspondence, and is closely interrelated with the Cartan matrix and Poincare series. The Coxeter functors constructed by Bernstein, Gelfand and Ponomarev plays a distinguished role in the representation theory of quivers.

On these pages, the ideas and formulas due to...

Graph models are extremely useful for almost all applications and applicators as they play an important role as structuring tools. They allow to model net structures - like roads, computers, telephones - instances of abstract data structures - like lists, stacks, trees - and functional or object oriented programming. In turn, graphs are models for mathematical objects, like categories and functors.

This highly self-contained book about algebraic graph theory is written with a view to keep the lively and unconventional atmosphere of a spoken text to communicate the enthusiasm the...

Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers.

Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses...

This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on...