Induced Modules over Group Algebras, Volume 161

1st Edition

Authors: G. Karpilovsky
Hardcover ISBN: 9780444884145
eBook ISBN: 9780080872728
Imprint: North Holland
Published Date: 1st March 1990
Page Count: 519
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Table of Contents

General Properties of Induced Modules. Induction from Normal Subgroups. Projective Summands of Induced Modules. Green Theory. Simple Induction and Restriction Pairs. Permutation Modules. Permutation Lattices. Bibliography. Notation. Index.

Description

In 1898 Frobenius discovered a construction which, in present terminology, associates with every module of a subgroup the induced module of a group. This construction proved to be of fundamental importance and is one of the basic tools in the entire theory of group representations.

This monograph is designed for research mathematicians and advanced graduate students and gives a picture of the general theory of induced modules as it exists at present. Much of the material has until now been available only in research articles. The approach is not intended to be encyclopedic, rather each topic is considered in sufficient depth that the reader may obtain a clear idea of the major results in the area.

After establishing algebraic preliminaries, the general facts about induced modules are provided, as well as some of their formal properties, annihilators and applications. The remaining chapters include detailed information on the process of induction from normal subgroups, projective summands of induced modules, some basic results of the Green theory with refinements and extensions, simple induction and restriction pairs and permutation modules. The final chapter is based exclusively on the work of Weiss, presenting a number of applications to the isomorphism problem for group rings.


Details

No. of pages:
519
Language:
English
Copyright:
© North Holland 1990
Published:
Imprint:
North Holland
eBook ISBN:
9780080872728
Hardcover ISBN:
9780444884145

Reviews

@from:M. Klemm @qu:This monograph is designed for research mathematicians and advanced graduate students and presents much material that has heretofore been available in research articles. @source:Mathematical Reviews


About the Authors

G. Karpilovsky Author

Affiliations and Expertise

California State University, Department of Mathematics, Chico, CA, USA