On the local structure of Morita and Rickard equivalences between Brauer blocks

"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. This description requires a new induction procedure and the introduction of suitable graded differential algebras. It leads to strong consequences such as the facts that the nilpotent blocks form a union of classes and that the basic Rickard equivalences preserve defect groups and Brauer categories." "Although the book reaches the most advanced level, a special effort has been made to make it accessible to graduate students interested in finite groups or noncommutative algebras. A full chapter is devoted to reviewing the terminology, and the particular case of Morita equivalences is discussed separately, as an introduction. Two appendices, one on Weiss's criterion for permutation modules and the other on tensor induction of graded differential algebras, are of interest on their own."--Jacket.