Atjaunināt sīkdatņu piekrišanu

E-grāmata: Quiver Representations

5.00/5 (8 ratings by Goodreads)
  • Formāts: PDF+DRM
  • Sērija : CMS Books in Mathematics
  • Izdošanas datums: 04-Sep-2014
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319092041
Citas grāmatas par šo tēmu:
  • Formāts - PDF+DRM
  • Cena: 53,52 €*
  • * ši ir gala cena, t.i., netiek piemērotas nekādas papildus atlaides
  • Ielikt grozā
  • Pievienot vēlmju sarakstam
  • Šī e-grāmata paredzēta tikai personīgai lietošanai. E-grāmatas nav iespējams atgriezt un nauda par iegādātajām e-grāmatām netiek atmaksāta.
Quiver RepresentationsPalielināt
  • Formāts: PDF+DRM
  • Sērija : CMS Books in Mathematics
  • Izdošanas datums: 04-Sep-2014
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319092041
Citas grāmatas par šo tēmu:

DRM restrictions

  • Kopēšana (kopēt/ievietot):

    nav atļauts

  • Drukāšana:

    nav atļauts

  • Lietošana:

    Digitālo tiesību pārvaldība (Digital Rights Management (DRM))
    Izdevējs ir piegādājis šo grāmatu šifrētā veidā, kas nozīmē, ka jums ir jāinstalē bezmaksas programmatūra, lai to atbloķētu un lasītu. Lai lasītu šo e-grāmatu, jums ir jāizveido Adobe ID. Vairāk informācijas šeit. E-grāmatu var lasīt un lejupielādēt līdz 6 ierīcēm (vienam lietotājam ar vienu un to pašu Adobe ID).

    Nepieciešamā programmatūra
    Lai lasītu šo e-grāmatu mobilajā ierīcē (tālrunī vai planšetdatorā), jums būs jāinstalē šī bezmaksas lietotne: PocketBook Reader (iOS / Android)

    Lai lejupielādētu un lasītu šo e-grāmatu datorā vai Mac datorā, jums ir nepieciešamid Adobe Digital Editions (šī ir bezmaksas lietotne, kas īpaši izstrādāta e-grāmatām. Tā nav tas pats, kas Adobe Reader, kas, iespējams, jau ir jūsu datorā.)

    Jūs nevarat lasīt šo e-grāmatu, izmantojot Amazon Kindle.

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.

Recenzijas

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)

Part I Quivers and Their Representations
1 Representations of Quivers
3(30)
1.1 Definitions and Examples
3(7)
1.1.1 Representations
3(2)
1.1.2 Morphisms
5(5)
1.2 Direct Sums and Indecomposable Representations
10(2)
1.3 Kernels, Cokernels, and Exact Sequences
12(7)
1.4 Horn Functors
19(4)
1.5 First Examples of Auslander-Reiten Quivers
23(10)
Problems
26(7)
2 Projective and Injective Representations
33(36)
2.1 Simple, Projective, and Injective Representations
36(9)
2.2 Projective Resolutions and Radicals of Projectives
45(9)
2.3 Auslander-Reiten Translation
54(8)
2.3.1 Duality
55(1)
2.3.2 Nakayama Functor
56(5)
2.3.3 The Auslander--Reiten Translations τ, τ-1
61(1)
2.4 Extensions and Ext
62(7)
Problems
66(3)
3 Examples of Auslander--Reiten Quivers
69(40)
3.1 Auslander--Reiten Quivers of Type An
70(12)
3.1.1 The Knitting Algorithm
70(2)
3.1.2 τ-Orbits
72(3)
3.1.3 Diagonals of a Polygon with N + 3 Vertices
75(3)
3.1.4 Computing Horn Dimensions, Ext Dimensions, and Short Exact Sequences
78(4)
3.2 Representation Type
82(2)
3.2.1 Gabriel's Theorem: Finite Representation Type
82(2)
3.3 Auslander-Reiten Quivers of Type Dn
84(12)
3.3.1 The Knitting Algorithm
84(2)
3.3.2 τ-Orbits
86(2)
3.3.3 Arcs of a Punctured Polygon with N Vertices
88(4)
3.3.4 Computing Horn Dimensions, Ext Dimensions, and Short Exact Sequences
92(4)
3.4 Representations of Bound Quivers: Quivers with Relations
96(7)
3.4.1 Cluster-Tilted Bound Quivers of Type An
97(3)
3.4.2 Cluster-Tilted Bound Quivers of Type Dn
100(3)
3.5 Notes
103(6)
Problems
103(6)
Part II Path Algebras
4 Algebras and Modules
109(24)
4.1 Concepts from Ring Theory
109(3)
4.2 Algebras
112(5)
4.3 Modules
117(4)
4.4 Idempotents and Direct Sum Decomposition
121(3)
4.5 A Criterion for Indecomposability
124(4)
4.6 Notes
128(5)
Problems
128(5)
5 Bound Quiver Algebras
133(20)
5.1 Admissible Ideals and Quotients of Path Algebras
133(3)
5.2 Equivalence of the Categories rep (Q, I) and mod K Q/I
136(2)
5.3 Projective Representations of Bound Quivers
138(4)
5.4 Homological Dimensions
142(2)
5.5 Auslander--Reiten Quivers of Bound Quiver Algebras
144(9)
Problems
150(3)
6 New Algebras from Old
153(22)
6.1 Tilted Algebras
154(5)
6.2 Trivial Extensions
159(1)
6.3 Self-Injective Algebras and the Trivial Extensions A DA
160(5)
6.4 Cluster-Tilted Algebras
165(4)
6.5 Triangular Matrix Algebras
169(1)
6.6 One-Point Extensions
170(2)
6.7 Notes
172(3)
Problems
172(3)
7 Auslander-Reiten Theory
175(28)
7.1 Almost Split Sequences
176(7)
7.2 Auslander--Reiten Translation
183(3)
7.3 Coxeter Transformation
186(4)
7.4 Auslander--Reiten Formulas
190(10)
7.4.1 Tensor Products
193(7)
7.5 Notes
200(3)
Problems
200(3)
8 Quadratic Forms and Gabriel's Theorem
203(20)
8.1 Variety of Representations
203(5)
8.2 Quadratic Form of a Quiver
208(7)
8.2.1 Classification of Positive Definite Quadratic Forms
210(5)
8.3 Roots
215(3)
8.3.1 Positive Roots in Type An
216(1)
8.3.2 Positive Roots in Type Dn
216(1)
8.3.3 Positive Roots in Type E6
217(1)
8.3.4 Positive Roots in Type E7
217(1)
8.3.5 Positive Roots in Type E8
217(1)
8.4 Gabriel's Theorem
218(3)
8.5 Notes
221(2)
Problems
221(2)
References 223(4)
Index 227
Ralf Schiffler is a Professor in the Department of Mathematics at the University of Connecticut.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
Permanent link: https://www.kriso.lv/db/97833190920412e.html
Keywords: