Groups of Exceptional Type, Coxeter Groups and Related Geometries

Groups of Exceptional Type, Coxeter Groups and Related Geometries PDF Author: N.S. Narasimha Sastry
Publisher: Springer Science & Business Media
ISBN: 8132218140
Category : Mathematics
Languages : en
Pages : 311

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Book Description
The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the book. Some of the articles provide the latest developments in the subject; some provide an overview of the current status of some important problems in this area; some survey an area highlighting the current developments; and some provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of the latest developments or to consider some problems for investigation.

Groups of Exceptional Type, Coxeter Groups and Related Geometries

Groups of Exceptional Type, Coxeter Groups and Related Geometries PDF Author: N.S. Narasimha Sastry
Publisher: Springer Science & Business Media
ISBN: 8132218140
Category : Mathematics
Languages : en
Pages : 311

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Book Description
The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the book. Some of the articles provide the latest developments in the subject; some provide an overview of the current status of some important problems in this area; some survey an area highlighting the current developments; and some provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of the latest developments or to consider some problems for investigation.

The Geometry and Topology of Coxeter Groups

The Geometry and Topology of Coxeter Groups PDF Author: Michael Davis
Publisher: Princeton University Press
ISBN: 0691131384
Category : Mathematics
Languages : en
Pages : 601

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Book Description
The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.

Reflection Groups and Coxeter Groups

Reflection Groups and Coxeter Groups PDF Author: James E. Humphreys
Publisher: Cambridge University Press
ISBN: 9780521436137
Category : Mathematics
Languages : en
Pages : 222

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Book Description
This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications.

Combinatorics of Coxeter Groups

Combinatorics of Coxeter Groups PDF Author: Anders Bjorner
Publisher: Springer Science & Business Media
ISBN: 3540275967
Category : Mathematics
Languages : en
Pages : 371

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Book Description
Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups

Group Theory and Computation

Group Theory and Computation PDF Author: N.S. Narasimha Sastry
Publisher: Springer
ISBN: 9811320470
Category : Mathematics
Languages : en
Pages : 213

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Book Description
This book is a blend of recent developments in theoretical and computational aspects of group theory. It presents the state-of-the-art research topics in different aspects of group theory, namely, character theory, representation theory, integral group rings, the Monster simple group, computational algorithms and methods on finite groups, finite loops, periodic groups, Camina groups and generalizations, automorphisms and non-abelian tensor product of groups. Presenting a collection of invited articles by some of the leading and highly active researchers in the theory of finite groups and their representations and the Monster group, with a focus on computational aspects, this book is of particular interest to researchers in the area of group theory and related fields of mathematics.

Algebraic Combinatorics and the Monster Group

Algebraic Combinatorics and the Monster Group PDF Author: Alexander A. Ivanov
Publisher: Cambridge University Press
ISBN: 1009338048
Category : Mathematics
Languages : en
Pages : 583

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Book Description
The current state of knowledge on the Monster group, including Majorana theory, Vertex Operator Algebras, Moonshine and maximal subgroups.

Finite Simple Groups: Thirty Years of the Atlas and Beyond

Finite Simple Groups: Thirty Years of the Atlas and Beyond PDF Author: Manjul Bhargava
Publisher: American Mathematical Soc.
ISBN: 1470436787
Category : Biography & Autobiography
Languages : en
Pages : 242

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Book Description
Classification of Finite Simple Groups, one of the most monumental accomplishments of modern mathematics, was announced in 1983 with the proof completed in 2004. Since then, it has opened up a new and powerful strategy to approach and resolve many previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the Atlas of Finite Groups (John H. Conway et al.), and in An Atlas of Brauer Characters (Christoph Jansen et al.). It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in the everyday life of researchers in many areas of contemporary mathematics. The main objective of the conference was to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. The papers in this volume are based on talks given at the conference. They present a comprehensive survey on current research in all of these fields.

Geometry Of Semilinear Embeddings: Relations To Graphs And Codes

Geometry Of Semilinear Embeddings: Relations To Graphs And Codes PDF Author: Mark Pankov
Publisher: World Scientific
ISBN: 9814651095
Category : Mathematics
Languages : en
Pages : 181

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Book Description
This volume covers semilinear embeddings of vector spaces over division rings and the associated mappings of Grassmannians. In contrast to classical books, we consider a more general class of semilinear mappings and show that this class is important. A large portion of the material will be formulated in terms of graph theory, that is, Grassmann graphs, graph embeddings, and isometric embeddings. In addition, some relations to linear codes will be described. Graduate students and researchers will find this volume to be self-contained with many examples.

Geometry of Coxeter Groups

Geometry of Coxeter Groups PDF Author: Howard Hiller
Publisher: Pitman Publishing
ISBN:
Category : Mathematics
Languages : en
Pages : 230

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Book Description


Groups of Lie Type and Their Geometries

Groups of Lie Type and Their Geometries PDF Author: William M. Kantor
Publisher: Cambridge University Press
ISBN: 052146790X
Category : Mathematics
Languages : en
Pages : 324

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Book Description
Silk Hope, NC is a buoyant and moving parable in which two good women find, among the hidden, forgotten virtues of the past, a sustenance to carry them into the future.