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

On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks
Author :
Publisher : Birkhäuser
Total Pages : 256
Release :
ISBN-10 : 9783034886932
ISBN-13 : 3034886934
Rating : 4/5 (934 Downloads)

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

Download or read book On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks written by Lluis Puig and published by Birkhäuser. This book was released on 2012-12-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


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