The Block Theory of Finite Group Algebras

Markus Linckelmann (City, University of London)

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English

Cambridge University Press
24 May 2018

Algebra; Number theory; Algebraic topology

Series: London Mathematical Society Student Texts

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.

By: Markus Linckelmann (City University of London)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: Volume 1
Dimensions: Height: 228mm, Width: 152mm, Spine: 28mm
Weight: 740g
ISBN: 9781108441834
ISBN 10: 1108441831
Series: London Mathematical Society Student Texts
Pages: 524
Publication Date: 24 May 2018
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

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

Reviews for The Block Theory of Finite Group Algebras

'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