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.
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"...a very welcome addition to the existing classical literature on representation theory and cohomology of finite groups....fascinating reading for someone who already has a basic knowledge of representation theory and cohomology ...I can recommend this book highly to anyone who works with representation theory and cohomology of finite groups." K. W. Roggenkamp, Mathematical Reviews
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Now in paperback this is the second of two volumes that will provide an introdcution 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 concentrates on the cohomology of groups, always with representations in view.
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Inside This Book
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First Sentence:
Groups representation are often studied as modules over the group algebra (see Chapter 3), which is a finite dimensional algebra in case the con-effecients are taken from a field, and a Noetherian ring if integer or p-adic coeffecients are used. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
dimensional symmetric algebra, vector space functor, finite representation type, tensor induction, projective indecomposable module, tame representation type, unique decomposition property, wild representation type, cyclic defect, exceptional vertex, subadditive function, irreducible maps, periodic module, projective relative, relative projectivity, psi operations, simple functor, path algebra, projective cover, sequence terminating, indecomposable representations, indecomposable modules, representation quiver, projective summand, admissible group New!
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Groups representation are often studied as modules over the group algebra (see Chapter 3), which is a finite dimensional algebra in case the con-effecients are taken from a field, and a Noetherian ring if integer or p-adic coeffecients are used. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
dimensional symmetric algebra, vector space functor, finite representation type, tensor induction, projective indecomposable module, tame representation type, unique decomposition property, wild representation type, cyclic defect, exceptional vertex, subadditive function, irreducible maps, periodic module, projective relative, relative projectivity, psi operations, simple functor, path algebra, projective cover, sequence terminating, indecomposable representations, indecomposable modules, representation quiver, projective summand, admissible group New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 4
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22
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- Lectures In Abstract Algebra by Nathan Jacobson in Back Matter
- Homological Algebra (PMS-19) by Henri Cartan in Back Matter
- From Now On by Marshall B Rosenberg on page 204
- Group Theory (Dover Books on Mathematics) by W. R. Scott in Back Matter
- Geometry and Cohomology in Group Theory (London Mathematical Society Lecture Note Series) by Peter H. Kropholler on page 73, and page 106
- Computational Methods for Representations of Groups and Algebras (Progress in Mathematics) by P. Dräxler on page 119, and page 232
- Representation Theory of Artin Algebras (Cambridge Studies in Advanced Mathematics) by Maurice Auslander in Back Matter
- A User's Guide to Spectral Sequences (Cambridge Studies in Advanced Mathematics) by John McCleary in Back Matter
- Computational Invariant Theory by Harm Derksen in Back Matter
See all 22 books citing this book
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