Classics Library
2 total works
Representation Theory of Finite Groups and Associative Algebras
by Charles W. Curtis and Irving Reiner
Published December 1962
This book offers a self-contained and up-to-date account of the representation theory of finite groups and associative rings and algebras. It pays particular attention to the theory of induced characters and induced representations, quasi-Frobenius rings and Frobenius algebras, integral representations, and the theory of modular representations. While emphasizing general methods and building the theory on the study of modules over rings with minimal condition, the book features enough examples and problems to help the researcher who needs to compute explicit representations for particular groups. In addition, the text includes some applications of group representations to the structure theory of finite groups, and a survey of current literature dealing with these applications. Neither encyclopedic nor historical in nature, this work concentrates instead on the most important and fruitful results, yet includes as much preliminary material as necessary for their proofs.
Revised and expanded, this second volume presents a modern treatment of finite groups and orders. It covers classical, modular and integral representation theory and contains many important new results. Beginning with an introductory review of ring theory, algebraic number theory, and homological algebra, the book then moves on to other topics such as modular representations and integral representation theory. Also covered are class groups and Picard groups, the theory of blocks, rationality questions, indecomposable modules and more.