Download or read book The Monster Group and Majorana Involutions written by Aleksandr Anatolievich Ivanov and published by Cambridge University Press. This book was released on 2009-03-19 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous construction and uniqueness proof for the Monster group, detailing its relation to Majorana involutions.

Download or read book Finite Simple Groups Thirty Years of the Atlas and Beyond written by Manjul Bhargava and published by American Mathematical Soc.. This book was released on 2017-07-24 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Algebraic Combinatorics and the Monster Group written by Alexander A. Ivanov and published by Cambridge University Press. This book was released on 2023-08-17 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering, arguably, one of the most attractive and mysterious mathematical objects, the Monster group, this text strives to provide an insightful introduction and the discusses the current state of the field. The Monster group is related to many areas of mathematics, as well as physics, from number theory to string theory. This book cuts through the complex nature of the field, highlighting some of the mysteries and intricate relationships involved. Containing many meaningful examples and a manual introduction to the computer package GAP, it provides the opportunity and resources for readers to start their own calculations. Some 20 experts here share their expertise spanning this exciting field, and the resulting volume is ideal for researchers and graduate students working in Combinatorial Algebra, Group theory and related areas.

Download or read book Groups of Exceptional Type Coxeter Groups and Related Geometries written by N.S. Narasimha Sastry and published by Springer Science & Business Media. This book was released on 2014-04-02 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Group Theory and Computation written by N.S. Narasimha Sastry and published by Springer. This book was released on 2018-09-21 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Recent Developments in Lie Algebras Groups and Representation Theory written by Kailash C. Misra and published by American Mathematical Soc.. This book was released on 2012 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the 2009-2011 Southeastern Lie Theory Workshop Series, held October 9-11, 2009 at North Carolina State University, May 22-24, 2010, at the University of Georgia, and June 1-4, 2011 at the University of Virginia. Some of the articles, written by experts in the field, survey recent developments while others include new results in Lie algebras, quantum groups, finite groups, and algebraic groups.

Download or read book The Finite Simple Groups written by Robert Wilson and published by Springer Science & Business Media. This book was released on 2009-12-14 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thisbookisintendedasanintroductiontoallthe?nitesimplegroups.During themonumentalstruggletoclassifythe?nitesimplegroups(andindeedsince), a huge amount of information about these groups has been accumulated. Conveyingthisinformationtothenextgenerationofstudentsandresearchers, not to mention those who might wish to apply this knowledge, has become a major challenge. With the publication of the two volumes by Aschbacher and Smith [12, 13] in 2004 we can reasonably regard the proof of the Classi?cation Theorem for Finite Simple Groups (usually abbreviated CFSG) as complete. Thus it is timely to attempt an overview of all the (non-abelian) ?nite simple groups in one volume. For expository purposes it is convenient to divide them into four basic types, namely the alternating, classical, exceptional and sporadic groups. The study of alternating groups soon develops into the theory of per- tation groups, which is well served by the classic text of Wielandt [170]and more modern treatments such as the comprehensive introduction by Dixon and Mortimer [53] and more specialised texts such as that of Cameron [19].

Download or read book The Mathieu Groups written by A. A. Ivanov and published by Cambridge University Press. This book was released on 2018-06-21 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathieu Groups are presented in the context of finite geometry and the theory of group amalgams.

Download or read book Group Cohomology and Algebraic Cycles written by Burt Totaro and published by Cambridge University Press. This book was released on 2014-06-26 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group cohomology reveals a deep relationship between algebra and topology, and its recent applications have provided important insights into the Hodge conjecture and algebraic geometry more broadly. This book presents a coherent suite of computational tools for the study of group cohomology and algebraic cycles. Early chapters synthesize background material from topology, algebraic geometry, and commutative algebra so readers do not have to form connections between the literatures on their own. Later chapters demonstrate Peter Symonds's influential proof of David Benson's regularity conjecture, offering several new variants and improvements. Complete with concrete examples and computations throughout, and a list of open problems for further study, this book will be valuable to graduate students and researchers in algebraic geometry and related fields.

Download or read book Rigidity in Higher Rank Abelian Group Actions Volume 1 Introduction and Cocycle Problem written by Anatole Katok and published by Cambridge University Press. This book was released on 2011-06-16 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems.

Download or read book A Universal Construction for Groups Acting Freely on Real Trees written by Ian Chiswell and published by Cambridge University Press. This book was released on 2012-10-18 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of R-trees is a well-established and important area of geometric group theory and in this book the authors introduce a construction that provides a new perspective on group actions on R-trees. They construct a group RF(G), equipped with an action on an R-tree, whose elements are certain functions from a compact real interval to the group G. They also study the structure of RF(G), including a detailed description of centralizers of elements and an investigation of its subgroups and quotients. Any group acting freely on an R-tree embeds in RF(G) for some choice of G. Much remains to be done to understand RF(G), and the extensive list of open problems included in an appendix could potentially lead to new methods for investigating group actions on R-trees, particularly free actions. This book will interest all geometric group theorists and model theorists whose research involves R-trees.

Download or read book Representations of Elementary Abelian p Groups and Vector Bundles written by David J. Benson and published by Cambridge University Press. This book was released on 2017 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up to date study of recent progress in vector bundle methods in the representation theory of elementary abelian groups.

Download or read book Induced Representations of Locally Compact Groups written by Eberhard Kaniuth and published by Cambridge University Press. This book was released on 2013 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive presentation of the theories of induced representations and Mackey analysis applied to a wide variety of groups.

Download or read book Auxiliary Polynomials in Number Theory written by David Masser and published by Cambridge University Press. This book was released on 2016-07-21 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified account of a powerful classical method, illustrated by applications in number theory. Aimed at graduates and professionals.

Download or read book Modern Approaches to the Invariant Subspace Problem written by Isabelle Chalendar and published by Cambridge University Press. This book was released on 2011-08-18 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics.

Download or read book Ridge Functions written by Allan Pinkus and published by Cambridge University Press. This book was released on 2015-08-07 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the state of the art in the theory of ridge functions, providing a solid theoretical foundation.

Download or read book Fourier Integrals in Classical Analysis written by Christopher D. Sogge and published by Cambridge University Press. This book was released on 2017-04-27 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents Hörmander's propagation of singularities theorem and uses this to prove the Duistermaat–Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff.