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Representations Of Finite Dimensional Algebras

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Representations Of Finite Dimensional Algebras

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Author : Peter Gabriel
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-09-12

Representations Of Finite Dimensional Algebras written by Peter Gabriel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-12 with Mathematics categories.

From the reviews: "... [Gabriel and Roiter] are pioneers in this subject and they have included proofs for statements which in their opinions are elementary, those which will help further understanding and those which are scarcely available elsewhere. They attempt to take us up to the point where we can find our way in the original literature. ..." --The Mathematical Gazette

Representations Of Finite Dimensional Algebras

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Author : Hiroyuki Tachikawa
language : en
Publisher: American Mathematical Soc.
Release Date : 1991

Representations Of Finite Dimensional Algebras written by Hiroyuki Tachikawa and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.

This volume contains the proceedings of the Tsukuba International Conference on Representations of Algebras and Related Topics (fifth ICRA), held at the University of Tsukuba, August 13-18, 1990. The conference focused on the rapid development of research on representations of finite-dimensional algebras and group representations. A subset of the fifty-seven lectures are collected here, together with a number of other papers not originally presented at the conference. With contributions by some of the world's leading experts in this area, this book provides a valuable overview of the frontier of research in representations of algebras.

Representations Of Finite Dimensional Algebras

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Author : Peter Gabriel
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-10-08

Representations Of Finite Dimensional Algebras

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Author : Peter Gabriel
language : en
Publisher: Springer
Release Date : 1997

Representations Of Finite Dimensional Algebras written by Peter Gabriel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

Triangulated Categories In The Representation Theory Of Finite Dimensional Algebras

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Author : Dieter Happel
language : en
Publisher:
Release Date : 1988

Triangulated Categories In The Representation Theory Of Finite Dimensional Algebras written by Dieter Happel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Electronic books categories.

This book is an introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras. In recent years representation theory has been an area of intense research and the author shows that derived categories of finite-dimensional algebras are a useful tool in studying tilting processes. Results on the structure of derived categories of hereditary algebras are used to investigate Dynkin algebras and interated tilted algebras. The author shows how triangulated categories arise naturally in the study of Frobenius categories. The study of trivial extension algebras and repetitive algebras is then developed using the triangulated structure on the stable category of the algebra's module category. With a comprehensive reference section, algebraists and research students in this field will find this an indispensable account of the theory of finite-dimensional algebras.

Representations Of Finite Dimensional Algebras

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Author : Peter Gabriel
language : en
Publisher:
Release Date : 1991

Representations Of Finite Dimensional Algebras written by Peter Gabriel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.

Triangulated Categories In The Representation Theory Of Finite Dimensional Algebras

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Author : Dieter Happel
language : en
Publisher: Cambridge University Press
Release Date : 1988

Triangulated Categories In The Representation Theory Of Finite Dimensional Algebras written by Dieter Happel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.

An introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras.

Representation Theory

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Author : Alexander Zimmermann
language : en
Publisher: Springer
Release Date : 2014-08-15

Representation Theory written by Alexander Zimmermann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-15 with Mathematics categories.

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.

A Journey Through Representation Theory

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Author : Caroline Gruson
language : en
Publisher: Springer
Release Date : 2018-10-23

A Journey Through Representation Theory written by Caroline Gruson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-23 with Mathematics categories.

This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.

Basic Representation Theory Of Algebras

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Author : Ibrahim Assem
language : en
Publisher: Springer Nature
Release Date : 2020-04-03

Basic Representation Theory Of Algebras written by Ibrahim Assem and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-03 with Mathematics categories.

This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander–Reiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the Auslander–Reiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representation-finite algebras, which are now the best understood class of algebras. Intended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book.

Representations Of Finite Dimensional Algebras

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