On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks
Brauer had already introduced the defect of a block and opened the way towards a classification by solving all the problems in defects zero and one, and by providing some evidence for the finiteness of the set of blocks with a given defect. In 1959 he discovered the defect group, and in 1964 Dade determined the blocks with cyclic defect groups.

In 1978 Alperin and Broué discovered the Brauer category, and Broué and the author determined the blocks having a nilpotent Brauer category. In 1979, the author discovered the source algebra which determines all the other current invariants, representing faithfully the block – and found its structure in the nilpotent blocks. Recently, the discovery by Rickard that all blocks with the same cyclic defect group and the same Brauer category have the same homotopic category focussed great interest on the new, loose relationship between blocks called Rickard equivalence.

This book describes the source algebra of a block from the source algebra of a Rickard equivalent block and the source of the Rickard equivalence.

1029886453
On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks
Brauer had already introduced the defect of a block and opened the way towards a classification by solving all the problems in defects zero and one, and by providing some evidence for the finiteness of the set of blocks with a given defect. In 1959 he discovered the defect group, and in 1964 Dade determined the blocks with cyclic defect groups.

In 1978 Alperin and Broué discovered the Brauer category, and Broué and the author determined the blocks having a nilpotent Brauer category. In 1979, the author discovered the source algebra which determines all the other current invariants, representing faithfully the block – and found its structure in the nilpotent blocks. Recently, the discovery by Rickard that all blocks with the same cyclic defect group and the same Brauer category have the same homotopic category focussed great interest on the new, loose relationship between blocks called Rickard equivalence.

This book describes the source algebra of a block from the source algebra of a Rickard equivalent block and the source of the Rickard equivalence.

54.99 In Stock
On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks

On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks

by Lluis Puig
On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks

On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks

by Lluis Puig

Paperback(Softcover reprint of the original 1st ed. 1999)

$54.99 
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Overview

Brauer had already introduced the defect of a block and opened the way towards a classification by solving all the problems in defects zero and one, and by providing some evidence for the finiteness of the set of blocks with a given defect. In 1959 he discovered the defect group, and in 1964 Dade determined the blocks with cyclic defect groups.

In 1978 Alperin and Broué discovered the Brauer category, and Broué and the author determined the blocks having a nilpotent Brauer category. In 1979, the author discovered the source algebra which determines all the other current invariants, representing faithfully the block – and found its structure in the nilpotent blocks. Recently, the discovery by Rickard that all blocks with the same cyclic defect group and the same Brauer category have the same homotopic category focussed great interest on the new, loose relationship between blocks called Rickard equivalence.

This book describes the source algebra of a block from the source algebra of a Rickard equivalent block and the source of the Rickard equivalence.


Product Details

ISBN-13: 9783034897327
Publisher: Birkhäuser Basel
Publication date: 10/16/2012
Series: Progress in Mathematics , #178
Edition description: Softcover reprint of the original 1st ed. 1999
Pages: 261
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

1 Introduction.- 2 General notation, terminology and quoted results.- 3 Noninjective induction of OG-interior algebras.- 4 Hecke OG-interior algebras and noninjective induction.- 5 On the local structure of Hecke OG-interior algebras.- 6 Morita stable equivalences between Brauer blocks.- 7 Basic Morita stable equivalences between Brauer blocks.- 8 The Morita stable equivalent class of a nilpotent block.- 9 The differential Z-grading O-algebra.- 10 DG-modules.- 11 D-algebras and DG-interior algebras.- 12 Induction of DG-interior algebras.- 13 Brauer sections in basic induced DG-interior algebras.- 14 Pointed groups on DG>-interior algebras and Higman embeddings.- 15 Hecke DG-interior algebras and noninjective induction.- 16 On the local structure of Hecke DG-interior algebras.- 17 Brauer sections in basic Hecke DG-interior algebras.- 18 Rickard equivalences between Brauer blocks.- 19 Basic Rickard equivalences between Brauer blocks.- References.
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