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Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras (Hardcover,... Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras (Hardcover, New)
D. J. Benson
R3,085 Discovery Miles 30 850 Ships in 10 - 15 working days

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.

Representations and Cohomology: Volume 2, Cohomology of Groups and Modules (Paperback, Volume 2, Cohomology of Groups and... Representations and Cohomology: Volume 2, Cohomology of Groups and Modules (Paperback, Volume 2, Cohomology of Groups and Modules)
D. J. Benson
R1,727 Discovery Miles 17 270 Ships in 10 - 15 working days

The heart of the book is a lengthy introduction to the representation theory of finite dimensional algebras, in which the techniques of quivers with relations and almost split sequences are discussed in some detail.

Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras (Paperback,... Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras (Paperback, Revised)
D. J. Benson
R1,560 Discovery Miles 15 600 Ships in 10 - 15 working days

This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules. Thus, Dr. Benson's unique perspective in this book incorporates homological algebra and the theory of representations of finite-dimensional algebras. This volume is primarily concerned with the exposition of the necessary background material, and the heart of the discussion 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 some detail.

Polynomial Invariants of Finite Groups (Paperback): D. J. Benson Polynomial Invariants of Finite Groups (Paperback)
D. J. Benson
R1,380 Discovery Miles 13 800 Ships in 10 - 17 working days

This book covers a topic of great interest in abstract algebra. It gives an account of invariant theory for the action of a finite group on the ring of polynomial functions on a linear representation, both in characteristic zero and characteristic p. Heavy use is made of techniques from commutative algebra, and these are developed as needed. Special attention is paid to the role played by pseudoreflections, which arise because they correspond to the divisors in the polynomial ring that ramify over the invariants. The author includes the recent proof of the Carlisle-Kropholler conjecture.

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