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Introduction to the Representation Theory of Algebras

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Item specifics

Condition
Brand New: A new, unread, unused book in perfect condition with no missing or damaged pages. See all condition definitionsopens in a new window or tab
subject_code
PBF
target_audience
College/University
is_adult_product
false
edition_number
1
binding
paperback
edition
2015
MPN
109 black & white illustrations, biograp
batteries_required
false
manufacturer
Springer
Brand
Springer
number_of_items
1
pages
192
genre
Algebra
part_number
109 black & white illustrations, biograp
publication_date
2015-01-14T00:00:01Z
unspsc_code
55101500
batteries_included
false
ISBN
9783319114743

About this product

Product Identifiers

Publisher
Springer International Publishing A&G
ISBN-10
3319114743
ISBN-13
9783319114743
eBay Product ID (ePID)
203885083

Product Key Features

Number of Pages
X, 179 Pages
Publication Name
Introduction to the Representation Theory of Algebras
Language
English
Subject
Algebra / Abstract, Algebra / General
Publication Year
2015
Type
Textbook
Subject Area
Mathematics
Author
Michael Barot
Format
Trade Paperback

Dimensions

Item Weight
105.6 Oz
Item Length
9.3 in
Item Width
6.1 in

Additional Product Features

Intended Audience
Scholarly & Professional
Reviews
"This book is a short and elementary course in the representation theory of finite dimensional algebras. It may be a good text book for undergraduate and PhD students, because only the knowledge of linear algebra is required." (Justyna Kosakowska, zbMATH 1330.16001, 2016) "Barot (former researcher, Instituto de Matemáticas, Univ. Nacional Autónoma de México) paints the big picture and emphasizes recent perspectives. ... An advanced undergraduate could read this book as a wonderful case study in the power of shifting viewpoints and thus an initiation into the modern practice of mathematics. ... Summing Up: Highly recommended. Lower- and upper-division undergraduates, graduate students, researchers/faculty, and professionals/practitioners." (D. V. Feldman, Choice, Vol. 53 (4), December, 2015) "The book gives a first introduction to the representation theory of finite-dimensional algebras over an algebraically closed field. ... With its well-chosen topics, arranged in a smooth and attractive order, the book is highly recommended as a one-semester introductory course on representations of finite-dimensional algebras." (Wolfgang Rump, Mathematical Reviews, October, 2015), "This book is a short and elementary course in the representation theory of finite dimensional algebras. It may be a good text book for undergraduate and PhD students, because only the knowledge of linear algebra is required." (Justyna Kosakowska, zbMATH 1330.16001, 2016) "Barot (former researcher, Instituto de Matemticas, Univ. Nacional Autnoma de Mxico) paints the big picture and emphasizes recent perspectives. ... An advanced undergraduate could read this book as a wonderful case study in the power of shifting viewpoints and thus an initiation into the modern practice of mathematics. ... Summing Up: Highly recommended. Lower- and upper-division undergraduates, graduate students, researchers/faculty, and professionals/practitioners." (D. V. Feldman, Choice, Vol. 53 (4), December, 2015) "The book gives a first introduction to the representation theory of finite-dimensional algebras over an algebraically closed field. ... With its well-chosen topics, arranged in a smooth and attractive order, the book is highly recommended as a one-semester introductory course on representations of finite-dimensional algebras." (Wolfgang Rump, Mathematical Reviews, October, 2015)
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
Matrix Problems.- Representations of Quivers.- Algebras.- Module Categories.- Elements of Homological Algebra.- The Auslander-Reiten Theory.- Knitting.- Combinatorial Invariants.- Indecomposables and Dimensions.
Synopsis
Matrix Problems.- Representations of Quivers.- Algebras.- Module Categories.- Elements of Homological Algebra.- The Auslander-Reiten Theory.- Knitting.- Combinatorial Invariants.- Indecomposables and Dimensions., This book gives a general introduction to the theory of representations of algebras. It starts with examples of classification problems of matrices under linear transformations, explaining the three common setups: representation of quivers, modules over algebras and additive functors over certain categories. The main part is devoted to (i) module categories, presenting the unicity of the decomposition into indecomposable modules, the Auslander-Reiten theory and the technique of knitting; (ii) the use of combinatorial tools such as dimension vectors and integral quadratic forms; and (iii) deeper theorems such as Gabriel's Theorem, the trichotomy and the Theorem of Kac - all accompanied by further examples. Each section includes exercises to facilitate understanding. By keeping the proofs as basic and comprehensible as possible and introducing the three languages at the beginning, this book is suitable for readers from the advanced undergraduate level onwards and enables them to consult related, specific research articles.
LC Classification Number
QA251.5

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