Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras PDF full book. Access full book title Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras by D. J. Benson. Download full books in PDF and EPUB format.
Author: D. J. Benson
Publisher: Cambridge University Press
ISBN: 9780521636537
Category : Mathematics
Languages : en
Pages : 260
Get Book Here
Book Description
An introduction to modern developments in the representation theory of finite groups and associative algebras.
Author: D. J. Benson
Publisher: Cambridge University Press
ISBN: 9780521636537
Category : Mathematics
Languages : en
Pages : 260
Get Book Here
Book Description
An introduction to modern developments in the representation theory of finite groups and associative algebras.
Author: David J. Benson
Publisher:
ISBN:
Category : Homology theory
Languages : en
Pages : 279
Get Book Here
Book Description
Author: D. J. Benson
Publisher: Cambridge University Press
ISBN: 9780521636520
Category : Mathematics
Languages : en
Pages : 296
Get Book Here
Book Description
A further introduction to modern developments in the representation theory of finite groups and associative algebras.
Author: D. J. Benson
Publisher: Cambridge University Press
ISBN: 9780521361347
Category : Mathematics
Languages : en
Pages : 260
Get Book Here
Book Description
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.
Author: Charles W. Curtis
Publisher: American Mathematical Soc.
ISBN: 9780821869451
Category : Mathematics
Languages : en
Pages : 722
Get Book Here
Book Description
Author: David J. Benson
Publisher:
ISBN:
Category : Homology theory
Languages : en
Pages : 279
Get Book Here
Book Description
Author: Alexander Zimmermann
Publisher: Springer
ISBN: 3319079689
Category : Mathematics
Languages : en
Pages : 720
Get Book Here
Book Description
Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.
Author: D. J. Benson
Publisher: Cambridge University Press
ISBN: 9780521636537
Category : Mathematics
Languages : en
Pages : 260
Get Book Here
Book Description
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.
Author: Ibrahim Assem
Publisher: Cambridge University Press
ISBN: 1139443186
Category : Mathematics
Languages : en
Pages : 34
Get Book Here
Book Description
This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of finite-oriented graphs (quivers) and homological algebra. The self-contained treatment constitutes an elementary, up-to-date introduction to the subject using, on the one hand, quiver-theoretical techniques and, on the other, tilting theory and integral quadratic forms. Key features include many illustrative examples, plus a large number of end-of-chapter exercises. The detailed proofs make this work suitable both for courses and seminars, and for self-study. The volume will be of great interest to graduate students beginning research in the representation theory of algebras and to mathematicians from other fields.
Author: Steven H. Weintraub
Publisher: American Mathematical Soc.
ISBN: 0821832220
Category : Mathematics
Languages : en
Pages : 226
Get Book Here
Book Description
``We explore widely in the valley of ordinary representations, and we take the reader over the mountain pass leading to the valley of modular representations, to a point from which (s)he can survey this valley, but we do not attempt to widely explore it. We hope the reader will be sufficiently fascinated by the scenery to further explore both valleys on his/her own.'' --from the Preface Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. In particular, representation theory has been one of the great tools in the study and classification of finite groups. There are some beautiful results that come from representation theory: Frobenius's Theorem, Burnside's Theorem, Artin's Theorem, Brauer's Theorem--all of which are covered in this textbook. Some seem uninspiring at first, but prove to be quite useful. Others are clearly deep from the outset. And when a group (finite or otherwise) acts on something else (as a set of symmetries, for example), one ends up with a natural representation of the group. This book is an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra. The approach is to develop the requisite algebra in reasonable generality and then to specialize it to the case of group representations. Methods and results particular to group representations, such as characters and induced representations, are developed in depth. Arithmetic comes into play when considering the field of definition of a representation, especially for subfields of the complex numbers. The book has an extensive development of the semisimple case, where the characteristic of the field is zero or is prime to the order of the group, and builds the foundations of the modular case, where the characteristic of the field divides the order of the group. The book assumes only the material of a standard graduate course in algebra. It is suitable as a text for a year-long graduate course. The subject is of interest to students of algebra, number theory and algebraic geometry. The systematic treatment presented here makes the book also valuable as a reference.
