Download Full eBooks in PDF
Groups Of Exceptional Type Coxeter Groups And Related Geometries Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Groups Of Exceptional Type Coxeter Groups And Related Geometries book. This book definitely worth reading, it is an incredibly well-written.
Author : N. S. Narasimha Sastry
Publisher : Unknown
Page : 320 pages
File Size : 41,7 Mb
Release : 2014-04-30
Category : Electronic
ISBN : 8132218159
Author : N.S. Narasimha Sastry
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 40,8 Mb
Release : 2014-04-02
Category : Mathematics
ISBN : 9788132218142
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.
Author : N.S. Narasimha Sastry,Manoj Kumar Yadav
Publisher : Springer
Page : 206 pages
File Size : 45,9 Mb
Release : 2018-09-21
Category : Mathematics
ISBN : 9789811320477
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.
Author : Mark Pankov
Publisher : World Scientific
Page : 180 pages
File Size : 50,9 Mb
Release : 2015-05-28
Category : Mathematics
ISBN : 9789814651097
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. Contents:Semilinear Mappings:Division Rings and Their HomomorphismsVector Spaces Over Division RingsSemilinear MappingsSemilinear EmbeddingsMappings of Grassmannians Induced by Semilinear EmbeddingsKreuzer's ExampleDualityCharacterization of Strong Semilinear EmbeddingsProjective Geometry and Linear Codes:Projective SpacesFundamental Theorem of Projective GeometryProof of Theorem 1.2m-independent Subsets in Projective SpacesPGL-subsetsGeneralized MacWilliams TheoremLinear CodesIsometric Embeddings of Grassmann Graphs:Graph TheoryElementary Properties of Grassmann GraphsEmbeddingsIsometric EmbeddingsProof of Theorem 3.1Equivalence of Isometric EmbeddingsLinearly Rigid Isometric EmbeddingsRemarks on Non-isometric EmbeddingsSome Results Related to Chow's TheoremHuang's TheoremJohnson Graph in Grassmann Graph:Johnson GraphIsometric Embeddings of Johnson Graphs in Grassmann GraphsProof of Theorem 4.2Classification Problem and Relations to Linear CodesCharacterizations of Apartments in Building GrassmanniansCharacterization of Isometric Embeddings:Main Result, Corollaries and RemarksCharacterization of DistanceConnectedness of the Apartment GraphIntersections of J(n, k)-subsets of Different TypesProof of Theorem 5.1Semilinear Mappings of Exterior Powers:Exterior PowersGrassmanniansGrassmann Codes Readership: Graduate students and researchers interested in the field of semilinear embeddings. Keywords:Semilinear Embedding;Grassmannian;Grassmann Graph;Linear Code
Author : Alexander A. Ivanov
Publisher : Cambridge University Press
Page : 583 pages
File Size : 47,8 Mb
Release : 2023-08-17
Category : Mathematics
ISBN : 9781009338042
The current state of knowledge on the Monster group, including Majorana theory, Vertex Operator Algebras, Moonshine and maximal subgroups.
Author : Howard Hiller
Publisher : Pitman Publishing
Page : 230 pages
File Size : 51,5 Mb
Release : 1982
Category : Mathematics
ISBN : UOM:39015049314548
Author : William M. Kantor,Lino Di Martino
Publisher : Unknown
Page : 320 pages
File Size : 54,7 Mb
Release : 1995
Category : Electronic books
ISBN : 110736700X
Presented here are papers from the 1993 Como meeting on groups of Lie type and their geometries.
Author : Manjul Bhargava,Robert Guralnick,Gerhard Hiss,Klaus Lux,Pham Huu Tiep
Publisher : American Mathematical Soc.
Page : 229 pages
File Size : 46,5 Mb
Release : 2017-07-24
Category : Atlas of finite groups
ISBN : 9781470436780
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.
Author : Michael Davis
Publisher : Princeton University Press
Page : 601 pages
File Size : 47,5 Mb
Release : 2008
Category : Mathematics
ISBN : 9780691131382
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.
Author : James E. Humphreys
Publisher : Cambridge University Press
Page : 222 pages
File Size : 40,5 Mb
Release : 1992-10
Category : Mathematics
ISBN : 0521436133
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.
Author : William M. Kantor,Lino Di Martino,J W S Cassels,Savilian Professor of Geometry N J Hitchin
Publisher : Unknown
Page : 322 pages
File Size : 47,7 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107362091
Presented here are papers from the 1993 Como meeting on groups of Lie type and their geometries.
Author : C. Patrick Bahls
Publisher : World Scientific
Page : 192 pages
File Size : 41,9 Mb
Release : 2005
Category : Mathematics
ISBN : 9781860945540
The book is the first to give a comprehensive overview of the techniques and tools currently being used in the study of combinatorial problems in Coxeter groups. It is self-contained, and accessible even to advanced undergraduate students of mathematics.The primary purpose of the book is to highlight approximations to the difficult isomorphism problem in Coxeter groups. A number of theorems relating to this problem are stated and proven. Most of the results addressed here concern conditions which can be seen as varying degrees of uniqueness of representations of Coxeter groups. Throughout the investigation, the readers are introduced to a large number of tools in the theory of Coxeter groups, drawn from dozens of recent articles by prominent researchers in geometric and combinatorial group theory, among other fields. As the central problem of the book may in fact be solved soon, the book aims to go further, providing the readers with many techniques that can be used to answer more general questions. The readers are challenged to practice those techniques by solving exercises, a list of which concludes each chapter.
Author : William M. Kantor
Publisher : Cambridge University Press
Page : 324 pages
File Size : 41,8 Mb
Release : 1995-01-12
Category : Mathematics
ISBN : 9780521467902
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.
Author : Anne Thomas
Publisher : Unknown
Page : 128 pages
File Size : 40,8 Mb
Release : 2018
Category : MATHEMATICS
ISBN : 3037196890
Coxeter groups are groups generated by reflections, and they appear throughout mathematics. Tits developed the general theory of Coxeter groups in order to develop the theory of buildings. Buildings have interrelated algebraic, combinatorial and geometric structures, and are powerful tools for understanding the groups which act on them. These notes focus on the geometry and topology of Coxeter groups and buildings, especially nonspherical cases. The emphasis is on geometric intuition, and there are many examples and illustrations. Part I describes Coxeter groups and their geometric realisations, particularly the Davis complex, and Part II gives a concise introduction to buildings. This book will be suitable for mathematics graduate students and researchers in geometric group theory, as well as algebra and combinatorics. The assumed background is basic group theory, including group actions, and basic algebraic topology, together with some knowledge of Riemannian geometry.
Author : Gebhard Böckle,Wolfram Decker,Gunter Malle
Publisher : Springer
Page : 753 pages
File Size : 45,6 Mb
Release : 2018-03-22
Category : Mathematics
ISBN : 9783319705668
This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.
