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Quiver Representations

Ralf Schiffler (Autor)

Buch | Hardcover

XI, 230 Seiten

2014 | 2014
Springer International Publishing (Verlag)
978-3-319-09203-4 (ISBN)

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This book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel's Theorem. The language of category theory is developed along the way as needed.

Ralf Schiffler is a Professor in the Department of Mathematics at the University of Connecticut.

Part I: Quivers and their representations.- Representations of quivers.- Projective and injective representations.- Examples of Auslander-Reiten quivers.- Part II: Path algebras.- Algebras and modules.- Bound quiver algebras.- New algebras from old.- Auslander-Reiten theory.- Quadratic forms and Gabriel's theorem.

"This book is an excellent text for undergraduates or beginning graduate students. The virtues of the book can be amplified by an instructor willing to go faster for those who have some prior exposure to basic algebra, or to go slower for students starting ab ovo. Secondly, a non-expert (in representation theory of quivers) may also benefit from this book in several ways ... . a reader will enjoy the clear and concise overview preceding each chapter and section." (Alex Martsinkovsky, Mathematical Reviews, February, 2016)

"The book under review is an elementary introduction to the diagrammatic or quiver approach to the representation theory of finite-dimensional algebras. It is perhaps the first such textbook addressed to advanced undergraduates or beginning graduate students. ... Teaching a course from this book should be a pleasant experience. Sets of problems are provided at the end of every one of its chapters, and little notes point to the literature. For a motivated student, thebook is well suited for self-study." (Felipe Zaldivar, MAA Reviews, December, 2014)

Erscheint lt. Verlag	19.9.2014
Reihe/Serie	CMS Books in Mathematics
Zusatzinfo	XI, 230 p. 357 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	531 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
Schlagworte	Algebra • Associative algebra • Auslander-Reiten theory • combinatorics • Gabriel's theorem • Module • Quiver representation
ISBN-10	3-319-09203-0 / 3319092030
ISBN-13	978-3-319-09203-4 / 9783319092034
Zustand	Neuware