Lineare Darstellungen Endlicher Gruppen

Lineare Darstellungen endlicher Gruppen PDF Book Detail:
Author: Jean Pierre Serre
Publisher: Springer-Verlag
ISBN: 3322858634
Size: 77.46 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : de
Pages : 102
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Book Description:

An Introduction To Groups Groupoids And Their Representations

An Introduction to Groups  Groupoids and Their Representations PDF Book Detail:
Author: Alberto Ibort
Publisher: CRC Press
ISBN: 1351869566
Size: 54.14 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 18
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Book Description: This book offers an introduction to the theory of groupoids and their representations encompassing the standard theory of groups. Using a categorical language, developed from simple examples, the theory of finite groupoids is shown to knit neatly with that of groups and their structure as well as that of their representations is described. The book comprises numerous examples and applications, including well-known games and puzzles, databases and physics applications. Key concepts have been presented using only basic notions so that it can be used both by students and researchers interested in the subject. Category theory is the natural language that is being used to develop the theory of groupoids. However, categorical presentations of mathematical subjects tend to become highly abstract very fast and out of reach of many potential users. To avoid this, foundations of the theory, starting with simple examples, have been developed and used to study the structure of finite groups and groupoids. The appropriate language and notions from category theory have been developed for students of mathematics and theoretical physics. The book presents the theory on the same level as the ordinary and elementary theories of finite groups and their representations, and provides a unified picture of the same. The structure of the algebra of finite groupoids is analysed, along with the classical theory of characters of their representations. Unnecessary complications in the formal presentation of the subject are avoided. The book offers an introduction to the language of category theory in the concrete setting of finite sets. It also shows how this perspective provides a common ground for various problems and applications, ranging from combinatorics, the topology of graphs, structure of databases and quantum physics.

Automorphic Representations And L Functions For The General Linear Group

Automorphic Representations and L Functions for the General Linear Group  PDF Book Detail:
Author: Dorian Goldfeld
Publisher: Cambridge University Press
ISBN: 1139500139
Size: 18.56 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages :
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Book Description: This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory. The book includes concrete examples of global and local representations of GL(n), and presents their associated L-functions. In Volume 1, the theory is developed from first principles for GL(1), then carefully extended to GL(2) with complete detailed proofs of key theorems. Several proofs are presented for the first time, including Jacquet's simple and elegant proof of the tensor product theorem. In Volume 2, the higher rank situation of GL(n) is given a detailed treatment. Containing numerous exercises by Xander Faber, this book will motivate students and researchers to begin working in this fertile field of research.

Linear Algebra And Group Theory

Linear Algebra and Group Theory PDF Book Detail:
Author: V. I. Smirnov
Publisher: Courier Corporation
ISBN: 0486482227
Size: 17.58 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 464
View: 2800

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Book Description: "Derived from an encyclopedic six-volume survey, this accessible text by a prominent Soviet mathematician offers a concrete approach, with an emphasis on applications. Containing material not otherwise available to English-language readers, the three-part treatment covers determinants and systems of equations, matrix theory, and group theory. Problem sets, with hints and answers, conclude each chapter. 1961 edition"--Provided by publisher.

Bulletin

Bulletin PDF Book Detail:
Author: Institute of Mathematics and Its Applications
Publisher:
ISBN:
Size: 35.71 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages :
View: 262

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Book Description:

Introduction To Lie Algebras And Representation Theory

Introduction to Lie Algebras and Representation Theory PDF Book Detail:
Author: JAMES HUMPHREYS
Publisher: Springer Science & Business Media
ISBN: 9780387900537
Size: 20.70 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 173
View: 1774

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Book Description: This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.