Moonshine Of Finite Groups

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"Moonshine" of Finite Groups

Author : Koichiro Harada
Publisher : European Mathematical Society
ISBN 13 : 9783037190906
Total Pages : 88 pages
Book Rating : 4.1/5 (99 download)

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Book Synopsis "Moonshine" of Finite Groups by : Koichiro Harada

Download or read book "Moonshine" of Finite Groups written by Koichiro Harada and published by European Mathematical Society. This book was released on 2010 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an almost verbatim reproduction of the author's lecture notes written in 1983-84 at Ohio State University, Columbus. A substantial update is given in the bibliography. Over the last 20 plus years there has been energetic activity in the field of finite simple group theory related to the monster simple group. Most notably, influential works have been produced in the theory of vertex operator algebras from research that was stimulated by the moonshine of the finite groups. Still, we can ask the same questions now that we did 30-40 years ago: What is the monster simple group? Is it really related to the theory of the universe as it was vaguely so envisioned? What lies behind the moonshine phenomena of the monster group? It may appear that we have only scratched the surface. These notes are primarily reproduced for the benefit of readers who wish to start learning about modular functions used in moonshine.

Moonshine of Finite Groups

Author : Koichiro Harada
Publisher :
ISBN 13 :
Total Pages : 110 pages
Book Rating : 4.:/5 (466 download)

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Book Synopsis Moonshine of Finite Groups by : Koichiro Harada

Download or read book Moonshine of Finite Groups written by Koichiro Harada and published by . This book was released on 1985* with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Proceedings on Moonshine and Related Topics

Author : John McKay
Publisher : American Mathematical Soc.
ISBN 13 : 0821828797
Total Pages : 280 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Proceedings on Moonshine and Related Topics by : John McKay

Download or read book Proceedings on Moonshine and Related Topics written by John McKay and published by American Mathematical Soc.. This book was released on 2001 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Moonshine workshop held at the Centre de Recherches Mathematiques (CRM) in Montreal. In this volume, all the classical Moonshine themes are presented, namely the Monster simple group and other finite groups, automorphic functions and forms and related congruence groups, and vertex algebras and their representations. These topics appear in either a pure form or in a blend of algebraic geometry dealing with algebraic surfaces, Picard-Fuchsequations, and hypergeometric functions.

Moonshine beyond the Monster

Author : Terry Gannon
Publisher : Cambridge University Press
ISBN 13 : 1139457802
Total Pages : 422 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Moonshine beyond the Monster by : Terry Gannon

Download or read book Moonshine beyond the Monster written by Terry Gannon and published by Cambridge University Press. This book was released on 2006-09-07 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was originally published in 2006. Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras. Moonshine Beyond the Monster describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory, algebra, number theory, geometry and functional analysis. Containing over a hundred exercises, it is also a suitable textbook for graduate courses on Moonshine and as supplementary reading for courses on conformal field theory and string theory.

Finite Groups 2003

Author : Chat Yin Ho
Publisher : Walter de Gruyter
ISBN 13 : 3110198126
Total Pages : 434 pages
Book Rating : 4.1/5 (11 download)

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Book Synopsis Finite Groups 2003 by : Chat Yin Ho

Download or read book Finite Groups 2003 written by Chat Yin Ho and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a volume of research articles related to finite groups. Topics covered include the classification of finite simple groups, the theory of p-groups, cohomology of groups, representation theory and the theory of buildings and geometries. As well as more than twenty original papers on the latest developments, which will be of great interest to specialists, the volume contains several expository articles, from which students and non-experts can learn about the present state of knowledge and promising directions for further research. The Finite Groups 2003 conference was held in honor of John Thompson. The profound influence of his fundamental contributions is clearly visible in this collection of papers dedicated to him.

Vertex Operators in Mathematics and Physics

Author : J. Lepowsky
Publisher : Springer Science & Business Media
ISBN 13 : 146139550X
Total Pages : 484 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Vertex Operators in Mathematics and Physics by : J. Lepowsky

Download or read book Vertex Operators in Mathematics and Physics written by J. Lepowsky and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: James Lepowsky t The search for symmetry in nature has for a long time provided representation theory with perhaps its chief motivation. According to the standard approach of Lie theory, one looks for infinitesimal symmetry -- Lie algebras of operators or concrete realizations of abstract Lie algebras. A central theme in this volume is the construction of affine Lie algebras using formal differential operators called vertex operators, which originally appeared in the dual-string theory. Since the precise description of vertex operators, in both mathematical and physical settings, requires a fair amount of notation, we do not attempt it in this introduction. Instead we refer the reader to the papers of Mandelstam, Goddard-Olive, Lepowsky-Wilson and Frenkel-Lepowsky-Meurman. We have tried to maintain consistency of terminology and to some extent notation in the articles herein. To help the reader we shall review some of the terminology. We also thought it might be useful to supplement an earlier fairly detailed exposition of ours [37] with a brief historical account of vertex operators in mathematics and their connection with affine algebras. Since we were involved in the development of the subject, the reader should be advised that what follows reflects our own understanding. For another view, see [29].1 t Partially supported by the National Science Foundation through the Mathematical Sciences Research Institute and NSF Grant MCS 83-01664. 1 We would like to thank Igor Frenkel for his valuable comments on the first draft of this introduction.

Finite Groups--coming of Age

Author : John McKay
Publisher : American Mathematical Soc.
ISBN 13 : 0821850474
Total Pages : 362 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Finite Groups--coming of Age by : John McKay

Download or read book Finite Groups--coming of Age written by John McKay and published by American Mathematical Soc.. This book was released on 1985 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: These conference papers should dispel any post-classification pessimism about the future of the theory of finite simple groups. Having noted that the theory developed for the classification touches on so few other branches of mathematics, the editor focuses on research in finite simple groups not central to the classification and presents a broad context for the recent results in the field. The papers are aimed at researchers and graduate students in algebra. They pay special attention to current research in sporadic geometry, the Fischer-Griess Monster group, and moonshine. Though all the papers are of high research value, the following papers of unusual significance should be singled out: Frenkel, Lepowsky, and Meurman's construction of the Monster group $F_1$; Conway and Queen's computation of characters of $E_8({\bf C})$; Norton's proof of the uniqueness of the Monster; and Mason's exploration of moonshine.

The Arcata Conference on Representations of Finite Groups, Part 1

Author : Paul Fong
Publisher : American Mathematical Soc.
ISBN 13 : 082181477X
Total Pages : 501 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Arcata Conference on Representations of Finite Groups, Part 1 by : Paul Fong

Download or read book The Arcata Conference on Representations of Finite Groups, Part 1 written by Paul Fong and published by American Mathematical Soc.. This book was released on 1987 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in these proceedings of the 1986 Arcata Summer Institute bear witness to the extraordinarily vital and intense research in the representation theory of finite groups. The confluence of diverse mathematical disciplines has brought forth work of great scope and depth. Particularly striking is the influence of algebraic geometry and cohomology theory in the modular representation theory and the character theory of reductive groups over finite fields, and in the general modular representation theory of finite groups. The continuing developments in block theory and the general character theory of finite groups is noteworthy. The expository and research aspects of the Summer Institute are well represented by these papers.

Moonshine, the Monster, and Related Topics

Author : Chongying Dong
Publisher : American Mathematical Soc.
ISBN 13 : 0821803859
Total Pages : 382 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Moonshine, the Monster, and Related Topics by : Chongying Dong

Download or read book Moonshine, the Monster, and Related Topics written by Chongying Dong and published by American Mathematical Soc.. This book was released on 1996 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the proceedings of a Joint Summer Research Conference held at Mount Holyoke College in Jun 1994. As perhaps the first conference proceedings devoted exclusively to the subject known as "Moonshine", this work contains something for many mathematicians and physicists. Many of the results featured are not available elsewhere.

Vertex Operator Algebras and the Monster

Author : Igor Frenkel
Publisher : Academic Press
ISBN 13 : 0080874541
Total Pages : 563 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Vertex Operator Algebras and the Monster by : Igor Frenkel

Download or read book Vertex Operator Algebras and the Monster written by Igor Frenkel and published by Academic Press. This book was released on 1989-05-01 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."

Quilts: Central Extensions, Braid Actions, and Finite Groups

Author : Tim Hsu
Publisher : Springer
ISBN 13 : 3540455809
Total Pages : 189 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Quilts: Central Extensions, Braid Actions, and Finite Groups by : Tim Hsu

Download or read book Quilts: Central Extensions, Braid Actions, and Finite Groups written by Tim Hsu and published by Springer. This book was released on 2007-05-06 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quilts are 2-complexes used to analyze actions and subgroups of the 3-string braid group and similar groups. This monograph establishes the fundamentals of quilts and discusses connections with central extensions, braid actions, and finite groups. Most results have not previously appeared in a widely available form, and many results appear in print for the first time. This monograph is accessible to graduate students, as a substantial amount of background material is included. The methods and results may be relevant to researchers interested in infinite groups, moonshine, central extensions, triangle groups, dessins d'enfants, and monodromy actions of braid groups.

Selected Papers on Number Theory, Algebraic Geometry, and Differential Geometry

Author : Katsumi Nomizu
Publisher : American Mathematical Soc.
ISBN 13 : 9780821875117
Total Pages : 170 pages
Book Rating : 4.8/5 (751 download)

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Book Synopsis Selected Papers on Number Theory, Algebraic Geometry, and Differential Geometry by : Katsumi Nomizu

Download or read book Selected Papers on Number Theory, Algebraic Geometry, and Differential Geometry written by Katsumi Nomizu and published by American Mathematical Soc.. This book was released on 1994 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents papers that originally appeared in the Japanese journal Sugaku. The papers explore the relationship between number theory, algebraic geometry, and differential geometry.

Groups and Symmetries

Author : John P. Harnad
Publisher : American Mathematical Soc.
ISBN 13 : 0821870424
Total Pages : 387 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Groups and Symmetries by : John P. Harnad

Download or read book Groups and Symmetries written by John P. Harnad and published by American Mathematical Soc.. This book was released on with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Encyclopaedia of Mathematics

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9401512795
Total Pages : 639 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

How to Solve the Da Vinci Code

Author : Richard Elwes
Publisher : Quercus
ISBN 13 : 1623652499
Total Pages : 311 pages
Book Rating : 4.6/5 (236 download)

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Book Synopsis How to Solve the Da Vinci Code by : Richard Elwes

Download or read book How to Solve the Da Vinci Code written by Richard Elwes and published by Quercus. This book was released on 2013-11-05 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Can you outrun a bullet? How do you build an electronic brain? Could you slow down time? How do you unleash chaos? From Plato's classification of regular polyhedra to making a million on the stock market, How to Solve the Da Vinci Code gives you everything you need to understand how numbers work, and the impact they have on our lives every day.

Conformal Field Theory

Author : Yavuz Nutku
Publisher : CRC Press
ISBN 13 : 042998250X
Total Pages : 342 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Conformal Field Theory by : Yavuz Nutku

Download or read book Conformal Field Theory written by Yavuz Nutku and published by CRC Press. This book was released on 2018-03-14 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an understanding of conformal field theory and its importance to both statistical mechanics and string theory. It introduces the Wess-Zumino-Novokov-Witten (WZNW) models and their current algebras, the affine Kac-Moody algebras.

Strings, Gauge Fields, and the Geometry Behind

Author : Anton Rebhan
Publisher : World Scientific
ISBN 13 : 9814412546
Total Pages : 566 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Strings, Gauge Fields, and the Geometry Behind by : Anton Rebhan

Download or read book Strings, Gauge Fields, and the Geometry Behind written by Anton Rebhan and published by World Scientific. This book was released on 2013 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains exclusively invited contributions from collaborators of Maximilian Kreuzer, giving accounts of his scientific legacy and original articles from renowned theoretical physicists and mathematicians, including Victor Batyrev, Philip Candelas, Michael Douglas, Alexei Morozov, Joseph Polchinski, Peter van Nieuwenhuizen, and Peter West. Besides a collection of review and research articles from high-profile researchers in string theory and related fields of mathematics (in particular, algebraic geometry) which discuss recent progress in the exploration of string theory vacua and corresponding mathematical developments, this book contains a pedagogical account of the important work of Brandt, Dragon, and Kreuzer on classification of anomalies in gauge theories. This highly cited work, which is also quoted in the textbook of Steven Weinberg on quantum field theory, has not yet been presented in full detail except in private lecture notes by Norbert Dragon. Similarly, the software package PALP (Package for Analyzing Lattice Polytopes with applications to toric geometry), which has been incorporated in the SAGE (Software for Algebra and Geometry Experimentation) project, has not yet been documented in full detail. This book contains a user manual for a new thoroughly revised version of PALP. By including these two very useful original contributions, researchers in quantum field theory, string theory, and mathematics will find added value in a pedagogical presentation of the classification of quantum gauge field anomalies, and the accompanying comprehensive manual and tutorial for the powerful software package PALP.