Principal Structures and Methods of Representation Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821889671
Total Pages : 456 pages
Book Rating : 4.8/5 (896 download)

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Book Synopsis Principal Structures and Methods of Representation Theory by : Dmitriĭ Petrovich Zhelobenko

Download or read book Principal Structures and Methods of Representation Theory written by Dmitriĭ Petrovich Zhelobenko and published by American Mathematical Soc.. This book was released on with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topic of this book can be described as the theory of algebraic and topological structures admitting natural representations by operators in vector spaces. These structures include topological algebras, Lie algebras, topological groups, and Lie groups. The book is divided into three parts. Part I surveys general facts for beginners, including linear algebra and functional analysis. Part II considers associative algebras, Lie algebras, topological groups, and Lie groups,along with some aspects of ring theory and the theory of algebraic groups. The author provides a detailed account of classical results in related branches of mathematics, such as invariant integration and Lie's theory of connections between Lie groups and Lie algebras. Part III discusses semisimple Liealgebras and Lie groups, Banach algebras, and quantum groups. This is a useful text for a wide range of specialists, including graduate students and researchers working in mathematical physics and specialists interested in modern representation theory. It is suitable for independent study or supplementary reading. Also available from the AMS by this acclaimed author is Compact Lie Groups and Their Representations.

A Course in Finite Group Representation Theory

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Publisher : Cambridge University Press
ISBN 13 : 1107162394
Total Pages : 339 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis A Course in Finite Group Representation Theory by : Peter Webb

Download or read book A Course in Finite Group Representation Theory written by Peter Webb and published by Cambridge University Press. This book was released on 2016-08-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Introduction to Representation Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 0821853511
Total Pages : 240 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Introduction to Representation Theory by : Pavel I. Etingof

Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

Representations of Semisimple Lie Algebras in the BGG Category O

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Publisher : American Mathematical Soc.
ISBN 13 : 1470463261
Total Pages : 289 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Representations of Semisimple Lie Algebras in the BGG Category O by : James E. Humphreys

Download or read book Representations of Semisimple Lie Algebras in the BGG Category O written by James E. Humphreys and published by American Mathematical Soc.. This book was released on 2021-07-14 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first textbook treatment of work leading to the landmark 1979 Kazhdan–Lusztig Conjecture on characters of simple highest weight modules for a semisimple Lie algebra g g over C C. The setting is the module category O O introduced by Bernstein–Gelfand–Gelfand, which includes all highest weight modules for g g such as Verma modules and finite dimensional simple modules. Analogues of this category have become influential in many areas of representation theory. Part I can be used as a text for independent study or for a mid-level one semester graduate course; it includes exercises and examples. The main prerequisite is familiarity with the structure theory of g g. Basic techniques in category O O such as BGG Reciprocity and Jantzen's translation functors are developed, culminating in an overview of the proof of the Kazhdan–Lusztig Conjecture (due to Beilinson–Bernstein and Brylinski–Kashiwara). The full proof however is beyond the scope of this book, requiring deep geometric methods: D D-modules and perverse sheaves on the flag variety. Part II introduces closely related topics important in current research: parabolic category O O, projective functors, tilting modules, twisting and completion functors, and Koszul duality theorem of Beilinson–Ginzburg–Soergel.

Algebras and Representation Theory

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Publisher : Springer
ISBN 13 : 3319919989
Total Pages : 304 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Algebras and Representation Theory by : Karin Erdmann

Download or read book Algebras and Representation Theory written by Karin Erdmann and published by Springer. This book was released on 2018-09-07 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.

Representation Theory and Complex Geometry

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Publisher : Birkhauser
ISBN 13 : 0817637923
Total Pages : 495 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Representation Theory and Complex Geometry by : Neil Chriss

Download or read book Representation Theory and Complex Geometry written by Neil Chriss and published by Birkhauser. This book was released on 1997 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an overview of modern advances in representation theory from a geometric standpoint. The techniques developed are quite general and can be applied to other areas such as quantum groups, affine Lie groups, and quantum field theory.

Automorphic Forms on GL (3,TR)

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Publisher : Springer
ISBN 13 : 3540390553
Total Pages : 196 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Automorphic Forms on GL (3,TR) by : D. Bump

Download or read book Automorphic Forms on GL (3,TR) written by D. Bump and published by Springer. This book was released on 2006-12-08 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Representation and Invariance of Scientific Structures

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Publisher : Stanford Univ Center for the Study
ISBN 13 : 9781575863337
Total Pages : 536 pages
Book Rating : 4.8/5 (633 download)

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Book Synopsis Representation and Invariance of Scientific Structures by : Patrick Suppes

Download or read book Representation and Invariance of Scientific Structures written by Patrick Suppes and published by Stanford Univ Center for the Study. This book was released on 2002 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fundamental reason for using formal methods in the philosophy of science is the desirability of having a fixed frame of reference that may be used to organize the variety of doctrines at hand. This book—Patrick Suppes's major work, and the result of several decades of research—examines how set-theoretical methods provide such a framework, covering issues of axiomatic method, representation, invariance, probability, mechanics, and language, including research on brain-wave representations of words and sentences. This is a groundbreaking, essential text from a distinguished philosopher.

Applications of Finite Groups

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Publisher : Academic Press
ISBN 13 : 1483268969
Total Pages : 359 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Applications of Finite Groups by : J. S. Lomont

Download or read book Applications of Finite Groups written by J. S. Lomont and published by Academic Press. This book was released on 2014-05-12 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications of Finite Groups focuses on the applications of finite groups to problems of physics, including representation theory, crystals, wave equations, and nuclear and molecular structures. The book first elaborates on matrices, groups, and representations. Topics include abstract properties, applications, matrix groups, key theorem of representation theory, properties of character tables, simply reducible groups, tensors and invariants, and representations generated by functions. The text then examines applications and subgroups and representations, as well as subduced and induced representations, fermion annihilation and creation operators, crystallographic point groups, proportionality tensors in crystals, and nonrelativistic wave equations. The publication takes a look at space group representations and energy bands, symmetric groups, and applications. Topics include molecular and nuclear structures, multiplet splitting in crystalline electric fields, construction of irreducible representations of the symmetric groups, and reality of representations. The manuscript is a dependable source of data for physicists and researchers interested in the applications of finite groups.

Number-Theoretic Algorithms in Cryptography

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821840900
Total Pages : 274 pages
Book Rating : 4.8/5 (49 download)

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Book Synopsis Number-Theoretic Algorithms in Cryptography by : Oleg Nikolaevich Vasilenko

Download or read book Number-Theoretic Algorithms in Cryptography written by Oleg Nikolaevich Vasilenko and published by American Mathematical Soc.. This book was released on 2007 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic number theory is a rapidly developing branch of number theory, which, in addition to its mathematical importance, has substantial applications in computer science and cryptography. Among the algorithms used in cryptography, the following are especially important: algorithms for primality testing; factorization algorithms for integers and for polynomials in one variable; applications of the theory of elliptic curves; algorithms for computation of discrete logarithms; algorithms for solving linear equations over finite fields; and, algorithms for performing arithmetic operations on large integers. The book describes the current state of these and some other algorithms. It also contains extensive bibliography. For this English translation, additional references were prepared and commented on by the author.

Representations of Groups

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Publisher : Cambridge University Press
ISBN 13 : 1139489186
Total Pages : 471 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Representations of Groups by : Klaus Lux

Download or read book Representations of Groups written by Klaus Lux and published by Cambridge University Press. This book was released on 2010-07-01 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: The representation theory of finite groups has seen rapid growth in recent years with the development of efficient algorithms and computer algebra systems. This is the first book to provide an introduction to the ordinary and modular representation theory of finite groups with special emphasis on the computational aspects of the subject. Evolving from courses taught at Aachen University, this well-paced text is ideal for graduate-level study. The authors provide over 200 exercises, both theoretical and computational, and include worked examples using the computer algebra system GAP. These make the abstract theory tangible and engage students in real hands-on work. GAP is freely available from www.gap-system.org and readers can download source code and solutions to selected exercises from the book's web page.

Models and Methods in the Philosophy of Science: Selected Essays

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Publisher : Springer Science & Business Media
ISBN 13 : 9401723001
Total Pages : 506 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Models and Methods in the Philosophy of Science: Selected Essays by : Patrick Suppes

Download or read book Models and Methods in the Philosophy of Science: Selected Essays written by Patrick Suppes and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thirty-one papers collected in this volume represent most of the arti cles that I have published in the philosophy of science and related founda tional areas of science since 1970. The present volume is a natural succes sor to Studies in the Methodology and Foundations of Science, a collection of my articles published in 1969 by Reidel (now a part of Kluwer). The articles are arranged under five main headings. Part I contains six articles on general methodology. The topics range from formal methods to the plurality of science. Part II contains six articles on causality and explanation. The emphasis is almost entirely on probabilistic approaches. Part III contains six articles on probability and measurement. The impor tance of representation theorems for both probability and measurement is stressed. Part IV contains five articles on the foundations of physics. The first three articles are concerned with action at a distance and space and time, the last two with quantum mechanics. Part V contains eight articles on the foundations of psychology. This is the longest part and the articles reflect my continuing strong interest in the nature of learning and perception. Within each part the articles are arranged chronologically. I turn now to a more detailed overview of the content. The first article of Part I concerns the role of formal methods in the philosophy of science. Here I discuss what is the new role for formal methods now that the imperialism of logical positivism has disappeared.

Quantization And Coherent States Methods - Proceedings Of Xi Workshop On Geometric Methods In Physics

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Publisher : World Scientific
ISBN 13 : 9814522031
Total Pages : 256 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Quantization And Coherent States Methods - Proceedings Of Xi Workshop On Geometric Methods In Physics by : S Twareque Ali

Download or read book Quantization And Coherent States Methods - Proceedings Of Xi Workshop On Geometric Methods In Physics written by S Twareque Ali and published by World Scientific. This book was released on 1993-10-29 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the conference was to find common elements between quantization and coherent states, and quantization on Poisson manifolds. Topics included are coherent states, geometric quantization, phase space quantization, deformation and *-products and Berry's phase.

Homogenization

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821889701
Total Pages : 256 pages
Book Rating : 4.8/5 (897 download)

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Book Synopsis Homogenization by : Gregori A. Chechkin

Download or read book Homogenization written by Gregori A. Chechkin and published by American Mathematical Soc.. This book was released on with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on both classical results of homogenization theory and modern techniques developed over the past decade. The powerful techniques in partial differential equations are illustrated with many exercises and examples to enhance understanding of the material. Several of the modern topics that are presented have not previously appeared in any monograph.

Lectures on Gaussian Integral Operators and Classical Groups

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Publisher : European Mathematical Society
ISBN 13 : 9783037190807
Total Pages : 576 pages
Book Rating : 4.1/5 (98 download)

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Book Synopsis Lectures on Gaussian Integral Operators and Classical Groups by : Yu. A. Neretin

Download or read book Lectures on Gaussian Integral Operators and Classical Groups written by Yu. A. Neretin and published by European Mathematical Society. This book was released on 2011 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an elementary self-contained introduction to some constructions of representation theory and related topics of differential geometry and analysis. Topics covered include the theory of various Fourier-like integral operators such as Segal-Bargmann transforms, Gaussian integral operators in $L^2$ and in the Fock space, integral operators with theta-kernels, the geometry of real and $p$-adic classical groups and symmetric spaces. The heart of the book is the Weil representation of the symplectic group (real and complex realizations, relations with theta-functions and modular forms, $p$-adic and adelic constructions) and representations in Hilbert spaces of holomorphic functions of several complex variables. This book is addressed to graduate students and researchers in representation theory, differential geometry, and operator theory. Prerequisites are standard university courses in linear algebra, functional analysis, and complex analysis.

Lectures in Mathematical Statistics

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821889688
Total Pages : 346 pages
Book Rating : 4.8/5 (896 download)

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Book Synopsis Lectures in Mathematical Statistics by : I͡U. N. Linʹkov

Download or read book Lectures in Mathematical Statistics written by I͡U. N. Linʹkov and published by American Mathematical Soc.. This book was released on with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is intended for the advanced study of several topics in mathematical statistics. The first part of the book is devoted to sampling theory (from one-dimensional and multidimensional distributions), asymptotic properties of sampling, parameter estimation, sufficient statistics, and statistical estimates. The second part is devoted to hypothesis testing and includes the discussion of families of statistical hypotheses that can be asymptotically distinguished. In particular,the author describes goodness-of-fit and sequential statistical criteria (Kolmogorov, Pearson, Smirnov, and Wald) and studies their main properties. The book is suitable for graduate students and researchers interested in mathematical statistics. It is useful for independent study or supplementaryreading.

Operator Algebras and Geometry

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821889725
Total Pages : 174 pages
Book Rating : 4.8/5 (897 download)

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Book Synopsis Operator Algebras and Geometry by :

Download or read book Operator Algebras and Geometry written by and published by American Mathematical Soc.. This book was released on with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book is aimed at researchers and graduate students working in differential topology, differential geometry, and global analysis who are interested in learning about operator algebras."--BOOK JACKET.