This is the first of two volumes which will provide an introduction
to modern developments in the representation theory of finite
groups and associative algebras. The subject is viewed from the
perspective of homological algebra and the theory of
representations of finite dimensional algebras; the author
emphasises modular representations and the homological algebra
associated with their categories. This volume is self-contained and
independent of its successor, being primarily concerned with the
exposition of the necessary background material. The heart of the
book is a lengthy introduction to the (Auslander-Reiten)
representation theory of finite dimensional algebras, in which the
techniques of quivers with relations and almost split sequences are
discussed in detail. Much of the material presented here has never
appeared in book form. Consequently students and research workers
studying group theory and indeed algebra in general will be
grateful to Dr Benson for supplying an exposition of a good deal of
the essential results of modern representation theory.
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