The Block Theory of Finite Group Algebras by Markus Linckelmann (English) Paperb

Publisher Description

This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.

Author Biography

Markus Linckelmann is a Professor in the Department of Mathematics at City, University of London.

Table of Contents

Introduction; 1. Algebras and modules; 2. Functors between module categories; 3. Character theory; 4. Algebras over p-local rings; 5. Group algebras and modules over p-local rings; References; Index.

Review

'This 2-volume book is a very welcome addition to the existing literature in modular representation theory. It contains a wealth of material much of which is here presented in textbook form for the rst time. It gives an excellent overview of the state of the art in this fascinating subject and also of the many challenging and fundamental open problems. It is well written and will certainly become a standard reference.' Burkhard Klshammer, MathSciNet

Promotional

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

Review Quote

'This 2-volume book is a very welcome addition to the existing literature in modular representation theory. It contains a wealth of material much of which is here presented in textbook form for the First time. It gives an excellent overview of the state of the art in this fascinating subject and also of the many challenging and fundamental open problems. It is well written and will certainly become a standard reference.' Burkhard Kulshammer, MathSciNet

Promotional "Headline"

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

Description for Bookstore

Graduate students and researchers in modular representation theory, especially block theory, will find this systematic introduction indispensable. The two volumes include detailed treatments of classic material as well as more modern developments which have not appeared in any book before, giving readers a comprehensive overview of the subject.

Description for Library

Graduate students and researchers in modular representation theory, especially block theory, will find this systematic introduction indispensable. The two volumes include detailed treatments of classic material as well as more modern developments which have not appeared in any book before, giving readers a comprehensive overview of the subject.

Details