Quiver representations

Author(s)

    • Schiffler, Ralf

Bibliographic Information

Quiver representations

Ralf Schiffler

(CMS books in mathematics)

Springer, c2014

Available at  / 22 libraries

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Note

Includes bibliographical reference (p. 223-225) and index

Description and Table of Contents

Description

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.

Table of Contents

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.

by "Nielsen BookData"

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Details

  • NCID
    BB16816164
  • ISBN
    • 9783319092034
  • LCCN
    2014945363
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    New York
  • Pages/Volumes
    xi, 230 p.
  • Size
    25 cm
  • Parent Bibliography ID
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