Product Description
First published in 1962, this classic book remains a remarkably complete introduction to various aspects of the representation theory of finite groups. One of its main advantages is that the authors went far beyond the standard elementary representation theory, including a masterly treatment of topics such as general non-commutative algebras, Frobenius algebras, representations over non-algebraically closed fields and fields of non-zero characteristic, and integral representations. These and many other subjects are treated extremely thoroughly, starting with basic definitions and results and proceeding to many important and crucial developments. Numerous examples and exercises help the reader of this unsurpassed book to master this important area of mathematics. ... Read more

Book Description
The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T.W. Anderson The Statistical Analysis of Time Series T.S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I Richard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold M. S. Coxeter Introduction to Modern Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Bruno de Finetti Theory of Probability, Volume 1 Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research Amos de Shalit & Herman Feshbach Theoretical Nuclear Physics, Volume 1 —Nuclear Structure J. L. Doob Stochastic Processes Nelson Dunford & Jacob T. Schwartz Linear Operators, Part One, General Theory Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Two, Spectral Theory—Self Adjoint Operators in Hilbert Space Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Three, Spectral Operators Herman Feshbach Theoretical Nuclear Physics: Nuclear Reactions Bernard Friedman Lectures on Applications-Oriented Mathematics Gerald J. Hahn & Samuel S. Shapiro Statistical Models in Engineering Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume I—Methods and Applications Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume II—Theory Peter Henrici Applied and Computational Complex Analysis, Volume 1—Power Series—Integration—Conformal Mapping—Location of Zeros Peter Henrici Applied and Computational Complex Analysis, Volume 2—Special Functions—Integral Transforms—Asymptotics—Continued Fractions Peter Henrici Applied and Computational Complex Analysis, Volume 3—Discrete Fourier Analysis—Cauchy Integrals—Construction of Conformal Maps—Univalent Functions Peter Hilton & Yel-Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Erwin O. Kreyszig Introductory Functional Analysis with Applications William H. Louisell Quantum Statistical Properties of Radiation Ali Hasan Nayfeh Introduction to Perturbation Techniques Emanuel Parzen Modern Probability Theory and Its Applications P. M. Prenter Splines and Variational Methods Walter Rudin Fourier Analysis on Groups C. L. Siegel Topics in Complex Function Theory, Volume I—Elliptic Functions and Uniformization Theory C. L. Siegel Topics in Complex Function Theory, Volume II—Automorphic and Abelian Integrals C. L. Siegel Topics in Complex Function Theory, Volume III—Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry J. J. Stoker Water Waves: The Mathematical Theory with Applications J. J. Stoker Nonlinear Vibrations in Mechanical and Electrical Systems ... Read more

Book Description
This is a reissue of a classic text, which includes the author's own corrections and provides a very accessible, self contained introduction to the classical theory of orders and maximal orders over a Dedekind ring. It starts with a long chapter that provides the algebraic prerequisites for this theory, covering basic material on Dedekind domains, localizations and completions, as well as semisimple rings and separable algebras. This is followed by an introduction to the basic tools in studying orders, such as reduced norms and traces, discriminants, and localization of orders. The theory of maximal orders is then developed in the local case, first in a complete setting, and then over any discrete valuation ring. This paves the way to a chapter on the ideal theory in global maximal orders, with detailed expositions on ideal classes, the Jordan-Zassenhaus Theorem, and genera. This is followed by a chapter on Brauer groups and crossed product algebras, where Hasse's theory of cyclic algebras over local fields is presented in a clear and self-contained fashion. Assuming a couple of facts from class field theory, the book goes on to present the theory of simple algebras over global fields, covering in particular Eichler's Theorem on the ideal classes in a maximal order, as well as various results on the KO group and Picard group of orders. The rest of the book is devoted to a discussion of non-maximal orders, with particular emphasis on hereditary orders and group rings. The ideas collected in this book have found important applications in the smooth representation theory of reductive p-adic groups. This text provides a useful introduction to this wide range of topics. It is written at a level suitable for beginning postgraduate students, is highly suited to class teaching and provides a wealth of exercises. ... Read more

Book Description
The aim of the lectures is to provide an introduction to recentdevelopments in the theory of class groups and Picard groups.The techniques employed come from the three main areas:algebraic number theory, representation theory of algebras andorders, and algebraic $K$-theory. ... Read more