Oxford University Press G-Algebras and Modular Representation Theory (Oxford Mathematical Monographs)

This book gives a comprehensive treatment of the theory of G-Algebras and shows how it can be used to solve a number of problems about blocks, modules and almost split sequences. The new approach to modular representation theory of finite groups was developed mainly by Lluis Puig since the 1970s and has several characteristic features: unification of several theories (e.g. block theory and module theory) under a single concept, introduction of new invariants (e.g. source algebras and multiplicity modules) which shed new light on the whole, new point of view on some classical theorems (e.g. Brauer's second main theorem) yielding more precise results, deep structural results such as Puig's theory on nilpotent blocks.