عنوان

An introduction to quiver representations /

شابک

1470425564

شابک

9781470425562

عنوان اصلي

An introduction to quiver representations /

نام عام مواد

[Book]

نام نخستين پديدآور

Harm Derksen, Jerzy Weyman.

محل نشرو پخش و غیره

Providence, Rhode Island :

نام ناشر، پخش کننده و غيره

American Mathematical Society,

تاریخ نشرو بخش و غیره

[2017]

نام خاص و کميت اثر

x, 334 pages :

ساير جزييات

illustrations ;

ابعاد

27 cm.

عنوان فروست

Graduate studies in mathematics ;

مشخصه جلد

184

متن يادداشت

Includes bibliographical references (pages 331-334) and index.

متن يادداشت

Ch. 1. Introduction -- Ch. 2. Homological algebra of quiver representations -- Ch. 3. Finite dimensional algebras -- Ch. 4. Gabriel's theorem -- Ch. 5. Almost split sequences -- Ch. 6. Auslander-Reiten theory -- Ch. 7. Extended Dynkin quivers -- Ch. 8. Kac's theorem -- Ch. 9. Geometric Invariant Theory -- Ch. 10. Semi-invariants of quiver representations -- Ch. 11. Orthogonal categories and exceptional sequences -- Ch. 12. Cluster categories.

بدون عنوان

0

متن يادداشت

This book is an introduction to the representation theory of quivers and finite dimensional algebras. It gives a thorough and modern treatment of the algebraic approach based on Auslander-Reiten theory as well as the approach based on geometric invariant theory. The material in the opening chapters is developed starting slowly with topics such as homological algebra, Morita equivalence, and Gabriel's theorem. Next, the book presents Auslander-Reiten theory, including almost split sequences and the Auslander-Reiten transform, and gives a proof of Kac's generalization of Gabriel's theorem. Once this basic material is established, the book goes on with developing the geometric invariant theory of quiver representations. The book features the exposition of the saturation theorem for semi-invariants of quiver representations and its application to Littlewood-Richardson coefficients. In the final chapters, the book exposes tilting modules, exceptional sequences and a connection to cluster categories. The book is suitable for a graduate course in quiver representations and has numerous exercises and examples throughout the text. The book will also be of use to experts in such areas as representation theory, invariant theory and algebraic geometry, who want to learn about applications of quiver representations to their fields.

موضوع مستند نشده

Directed graphs.

موضوع مستند نشده

Representations of graphs.

موضوع مستند نشده

Vector spaces.

موضوع مستند نشده

Algebraic geometry-- Algebraic groups-- Geometric invariant theory.

موضوع مستند نشده

Associative rings and algebras-- Representation theory of rings and algebras-- Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers.

موضوع مستند نشده

Associative rings and algebras-- Representation theory of rings and algebras-- Representations of Artinian rings.

موضوع مستند نشده

Commutative algebra-- General commutative ring theory-- Actions of groups on commutative rings; invariant theory.

موضوع مستند نشده

Directed graphs.

موضوع مستند نشده

Representations of graphs.

موضوع مستند نشده

Vector spaces.

شماره

ويراست

شماره رده

نشانه اثر

شماره رده

شماره رده

کد سيستم

کد سيستم

مستند نام اشخاص تاييد نشده

Derksen, Harm,1970-

مستند نام اشخاص تاييد نشده

Weyman, Jerzy,1955-

تاريخ عمليات

20200823025726.0

قواعد فهرست نويسي ( بخش توصيفي )

rda

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y