Based on the special summer session held at the Max Planck Institute for Mathematics and the Hausdorff Research Institute for Mathematics, this volume provides a window into various subjects related to reductive groups, including real and complex analysis on homogeneous spaces, arithmetic aspects of moment geometry, and geometry of flag varieties.
Presents the solutions to two problems: the first is the construction of expanding graphs - graphs which are of fundamental importance for communication networks and computer science, and the second is the Ruziewicz problem concerning the finitely additive invariant measures on spheres.
This book presents the solution of a long-standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on commutative algebra, cohomology of groups and stable homotopy theory.
Covers elementary results in Abelian Groups. This book covers many topics related to the theory. It offers exercises categorised according to their level of difficulty, simple, exercises of medium difficulty, difficult exercises, and their solutions. It is aimed at experts in the field as a reference to a large number of examples in Group Theory.
Presents a comprehensive treatment of Coxeter groups from the viewpoint of geometric group theory. This book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincare Conjecture; and Gromov's theory of CAT(0) spaces and groups.
Covers the theory of Lie groups, focusing on matrix groups: closed subgroups of real and complex general linear groups. This book studies examples and describes classical families of simply connected compact groups. It introduces the idea of a lie group and explores the associated notion of a homogeneous space using orbits of smooth actions.
The p-adic numbers and more generally local fields have become increasingly important in a range of mathematical disciplines, and are now seen as essential tools in many areas of mathematics, including number theory, algebraic geometry, group representation theory and algebraic topology.
This book covers the basics of representation theory for finite groups from the viewpoint of semisimple algebras and modules over them. The presentation interweaves specific examples with the development of powerful tools based on the notion of semisimplicity.
Offers an introduction to Lie theory, representation theory, invariant theory, and algebraic groups. This book presents the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. It is suitable for physicists as well as mathematicians.
The theory of abstract groups comes into play in areas like crystallography and quantum mechanics, geometry and topology, analysis and algebra, physics, chemistry, and even biology. Readers need to know high school mathematics, much of which is presented in this book, to grasp this important subject. It contains problems with solutions.
Group Theory has wide-ranging uses in the field of mathematics. This book offers a comprehensive account of the finite groups. It begins with the basic definitions and moves on to develop the theory, using examples to help students with their understanding.
Provides an introduction to the representation theory of the symmetric group from three different points of view: general representation theory, combinatorial algorithms, and symmetric functions. This book is suitable for graduate students and mathematicians in other specialties interested in finding out about this field.
Uses mathematical toys such as the Rubik's Cube to make abstract algebra and group theory fun. This book employs permutation puzzles, such as the 15 puzzle, the Rainbow Masterball, the Pyraminx, the Skewb, the Megaminx, Merlin's Machine, and variants of the Rubik's Cube to explain topics in introductory algebra and group theory.
Introduces the basics of K-theory, and explains details of the various concepts encountered en route to a deeper understanding of the subject. Exercises have also been included. Other subjects dealt with include: the classification of extensions of C*-algebras and the functional K-theory.
Based on the authors' lecture notes, this book is concerned with an aspect of graph theory that has broad applications to complexity theory, graph colourings, channel assignment and statistical physics. Containing exercises, hints and references, it is ideal for graduate students and researchers alike.
Explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language. This title includes chapters on the results including automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture.
The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed for readers approaching the subject for the first time, this book recaps the basic definitions and results, including Lagranges Theorem, the isomorphism theorems and group actions.
Presents a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality. This book describes Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it.
There has been a growing trend toward the utilization of teams for accomplishing work in organizations. Project teams, self-managed work teams and top management teams, among others have become a regular element in the corporation or military. This book presents an overview of the state of the art research on team effectiveness.
The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and their basic properties. The second half focuses specifically on the ring theoretic properties of polycyclic groups and their applications.
Quasi-Frobenius rings and Nakayama rings were introduced by T Nakayama in 1939. In 1978, M Harada introduced a new class of artinian rings which were later called Harada rings in his honour. This work intends to present the structure of Harada rings and provide important applications of this structure to the classical artinian rings.
This introduction to the theory of groups covers all topics likely to be encountered in undergraduate courses. The book takes as its theme the various fundamental classification theorems in finite group theory, and the text is further explained in numerous examples and exercises, and summaries at the end of each chapter.
Nearrings arise naturally in various ways, but most nearrings studied today are the endomorphisms of a group or co-group object of a category. This study covers those nearrings that are rings if the group object is also a co-group object, and explains their application to other branches of science.
Includes: R Baer: Complementation in finite gropus; M Lazard: Groupes, anneaux de Lie et probleme de Burnside; J Tits: Sur les groupes algebriques afffines; Theoremes fondamentaux de structure; and, Classification des groupes semisimples et geometries associees.
Group theory studies the algebraic structures known as groups. This book gathers the research in the study of group theory and highlights such topics as: application of symmetry analysis to the description of ordered structures in crystals, a survey of Lie Group analysis, graph groupoids and representations, and others.
Presents important results and topics in the theory of partially ordered groups, with proofs that rely on (and interplay with) other areas of mathematics. The book stresses both the special techniques of the discipline and the overlap with other areas of pure mathematics.
The theory of operator semigroups was essentially discovered in the early 1930s. This book focuses primarily on the theoretical connection between the theory of operator semigroups and spectral theory. It gives an account of the subject with numerous examples, detailed proofs, and a brief look at a few applications.
An introduction to topics in commutative algebra, with an emphasis on worked examples and applications. It combines algebraic theory with applications to number theory, problems in classical Greek geometry, and the theory of finite fields which has uses in other branches of science.
To help students learn at their own pace this book takes a programmed learning approach. The reader goes through a series of carefully constructed exercises, designed to lead them through the mathematics, and give them a full understanding of how this relates to the chemistry.
Written in the Socratic/Moore method, this book presents a sequence of problems which develop aspects in the field of semigroups of operators. The reader can discover important developments of the subject and quickly arrive at the point of independent research.
This book introduces a class of continuous Zd-actions diverse enough to exhibit many of the new phenomena encountered in the transition from Z to Zd, but which lends itself to systematic study: the Zd-actions by automorphisms of compact, abelian groups.