Triangulated categories in the representation theory of finite dimensional algebras /:
This book is an introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras. In recent years representation theory has been an area of intense research and the author shows that derived categories of finite-dimensional algebras are a useful tool...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1988.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
119. |
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | This book is an introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras. In recent years representation theory has been an area of intense research and the author shows that derived categories of finite-dimensional algebras are a useful tool in studying tilting processes. Results on the structure of derived categories of hereditary algebras are used to investigate Dynkin algebras and interated tilted algebras. The author shows how triangulated categories arise naturally in the study of Frobenius categories. The study of trivial extension algebras and repetitive algebras is then developed using the triangulated structure on the stable category of the algebra's module category. With a comprehensive reference section, algebraists and research students in this field will find this an indispensable account of the theory of finite-dimensional algebras. |
| Beschreibung: | 1 online resource (208 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781107361362 1107361362 9780511892271 0511892276 1139881760 9781139881760 1107366275 9781107366275 1107368448 9781107368446 1299404065 9781299404069 1107363810 9781107363816 0511629222 9780511629228 |
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| 245 | 1 | 0 | |a Triangulated categories in the representation theory of finite dimensional algebras / |c Dieter Happel. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 1988. | ||
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 119 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This book is an introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras. In recent years representation theory has been an area of intense research and the author shows that derived categories of finite-dimensional algebras are a useful tool in studying tilting processes. Results on the structure of derived categories of hereditary algebras are used to investigate Dynkin algebras and interated tilted algebras. The author shows how triangulated categories arise naturally in the study of Frobenius categories. The study of trivial extension algebras and repetitive algebras is then developed using the triangulated structure on the stable category of the algebra's module category. With a comprehensive reference section, algebraists and research students in this field will find this an indispensable account of the theory of finite-dimensional algebras. | ||
| 505 | 0 | |a Cover; Title; Copyright; Contents; Preface; CHAPTER I: Triangulated categories; 1. Foundations; 2. Frobenius categories; 3. Examples; 4. Auslander-Reiten triangles; 5. Description of some derived categories; CHAPTER II: Repetitive algebras; 1. t-categories; 2. Repetitive algebras; 3. Generating subcategories; 4. The main theorem; 5. Examples; CHAPTER III: Tilting theory; 1. Grothendieck groups of triangulated categories; 2. The invariance property; 3. The Brenner-Butler Theorem; 4. Torsion theories; 5. Tilted algebras; 6. Partial tilting modules; 7. Concealed algebras | |
| 505 | 8 | |a CHAPTER IV: Piecewise hereditary algebras1. Piecewise hereditary algebras; 2. Cycles in mod kZ?; 3. The representation-finite case; 4. Iterated tilted algebras; 5. The general case; 6. The Dynkin case; 7. The affine case; CHAPTER V: Trivial extension algebras; 1. Preliminaries; 2. The representation-finite case; 3. The representation-infinite case; References; Index | |
| 546 | |a English. | ||
| 650 | 0 | |a Triangulated categories. |0 http://id.loc.gov/authorities/subjects/sh2010007133 | |
| 650 | 0 | |a Representations of algebras. |0 http://id.loc.gov/authorities/subjects/sh85112938 | |
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| 650 | 0 | |a Categories (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85020992 | |
| 650 | 6 | |a Catégories (Mathématiques) | |
| 650 | 6 | |a Représentations des algèbres. | |
| 650 | 6 | |a Modules (Algèbre) | |
| 650 | 6 | |a Catégories triangulées. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Linear. |2 bisacsh | |
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| 650 | 7 | |a Modules (Algebra) |2 fast | |
| 650 | 7 | |a Representations of algebras |2 fast | |
| 650 | 7 | |a Triangulated categories |2 fast | |
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| 655 | 4 | |a Triangulierte Kategorie. | |
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| author | Happel, Dieter, 1953- |
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| contents | Cover; Title; Copyright; Contents; Preface; CHAPTER I: Triangulated categories; 1. Foundations; 2. Frobenius categories; 3. Examples; 4. Auslander-Reiten triangles; 5. Description of some derived categories; CHAPTER II: Repetitive algebras; 1. t-categories; 2. Repetitive algebras; 3. Generating subcategories; 4. The main theorem; 5. Examples; CHAPTER III: Tilting theory; 1. Grothendieck groups of triangulated categories; 2. The invariance property; 3. The Brenner-Butler Theorem; 4. Torsion theories; 5. Tilted algebras; 6. Partial tilting modules; 7. Concealed algebras CHAPTER IV: Piecewise hereditary algebras1. Piecewise hereditary algebras; 2. Cycles in mod kZ?; 3. The representation-finite case; 4. Iterated tilted algebras; 5. The general case; 6. The Dynkin case; 7. The affine case; CHAPTER V: Trivial extension algebras; 1. Preliminaries; 2. The representation-finite case; 3. The representation-infinite case; References; Index |
| ctrlnum | (OCoLC)839303205 |
| dewey-full | 512/.55 |
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| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
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In recent years representation theory has been an area of intense research and the author shows that derived categories of finite-dimensional algebras are a useful tool in studying tilting processes. Results on the structure of derived categories of hereditary algebras are used to investigate Dynkin algebras and interated tilted algebras. The author shows how triangulated categories arise naturally in the study of Frobenius categories. The study of trivial extension algebras and repetitive algebras is then developed using the triangulated structure on the stable category of the algebra's module category. With a comprehensive reference section, algebraists and research students in this field will find this an indispensable account of the theory of finite-dimensional algebras.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Cover; Title; Copyright; Contents; Preface; CHAPTER I: Triangulated categories; 1. Foundations; 2. Frobenius categories; 3. 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| genre | Triangulierte Kategorie. |
| genre_facet | Triangulierte Kategorie. |
| id | ZDB-4-EBA-ocn839303205 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-11T08:41:21Z |
| institution | BVB |
| isbn | 9781107361362 1107361362 9780511892271 0511892276 1139881760 9781139881760 1107366275 9781107366275 1107368448 9781107368446 1299404065 9781299404069 1107363810 9781107363816 0511629222 9780511629228 |
| language | English |
| oclc_num | 839303205 |
| open_access_boolean | |
| owner | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (208 pages) |
| psigel | ZDB-4-EBA FWS_PDA_EBA ZDB-4-EBA |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Happel, Dieter, 1953- https://id.oclc.org/worldcat/entity/E39PBJqFHJTpkGCQYqmd6yFYfq http://id.loc.gov/authorities/names/n87840476 Triangulated categories in the representation theory of finite dimensional algebras / Dieter Happel. Cambridge ; New York : Cambridge University Press, 1988. 1 online resource (208 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 119 Includes bibliographical references and index. Print version record. This book is an introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras. In recent years representation theory has been an area of intense research and the author shows that derived categories of finite-dimensional algebras are a useful tool in studying tilting processes. Results on the structure of derived categories of hereditary algebras are used to investigate Dynkin algebras and interated tilted algebras. The author shows how triangulated categories arise naturally in the study of Frobenius categories. The study of trivial extension algebras and repetitive algebras is then developed using the triangulated structure on the stable category of the algebra's module category. With a comprehensive reference section, algebraists and research students in this field will find this an indispensable account of the theory of finite-dimensional algebras. Cover; Title; Copyright; Contents; Preface; CHAPTER I: Triangulated categories; 1. Foundations; 2. Frobenius categories; 3. Examples; 4. Auslander-Reiten triangles; 5. Description of some derived categories; CHAPTER II: Repetitive algebras; 1. t-categories; 2. Repetitive algebras; 3. Generating subcategories; 4. The main theorem; 5. Examples; CHAPTER III: Tilting theory; 1. Grothendieck groups of triangulated categories; 2. The invariance property; 3. The Brenner-Butler Theorem; 4. Torsion theories; 5. Tilted algebras; 6. Partial tilting modules; 7. Concealed algebras CHAPTER IV: Piecewise hereditary algebras1. Piecewise hereditary algebras; 2. Cycles in mod kZ?; 3. The representation-finite case; 4. Iterated tilted algebras; 5. The general case; 6. The Dynkin case; 7. The affine case; CHAPTER V: Trivial extension algebras; 1. Preliminaries; 2. The representation-finite case; 3. The representation-infinite case; References; Index English. Triangulated categories. http://id.loc.gov/authorities/subjects/sh2010007133 Representations of algebras. http://id.loc.gov/authorities/subjects/sh85112938 Modules (Algebra) http://id.loc.gov/authorities/subjects/sh85086470 Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Catégories (Mathématiques) Représentations des algèbres. Modules (Algèbre) Catégories triangulées. MATHEMATICS Algebra Linear. bisacsh Categories (Mathematics) fast Modules (Algebra) fast Representations of algebras fast Triangulated categories fast Algebra gnd Darstellungstheorie gnd http://d-nb.info/gnd/4148816-7 Dimension n gnd http://d-nb.info/gnd/4309313-9 Kategorie Mathematik gnd http://d-nb.info/gnd/4129930-9 Triangulation gnd http://d-nb.info/gnd/4186017-2 Categorieën (wiskunde) gtt Associatieve ringen. gtt Algebra associativa. larpcal Algebra homologica. larpcal Représentations d'algèbres. ram Modules (algèbre) ram Catégories (mathématiques) ram Triangulierte Kategorie. Print version: Happel, Dieter, 1953- Triangulated categories in the representation theory of finite dimensional algebras. Cambridge ; New York : Cambridge University Press, 1988 0521339227 (DLC) 87030100 (OCoLC)16921558 London Mathematical Society lecture note series ; 119. http://id.loc.gov/authorities/names/n42015587 |
| spellingShingle | Happel, Dieter, 1953- Triangulated categories in the representation theory of finite dimensional algebras / London Mathematical Society lecture note series ; Cover; Title; Copyright; Contents; Preface; CHAPTER I: Triangulated categories; 1. Foundations; 2. Frobenius categories; 3. Examples; 4. Auslander-Reiten triangles; 5. Description of some derived categories; CHAPTER II: Repetitive algebras; 1. t-categories; 2. Repetitive algebras; 3. Generating subcategories; 4. The main theorem; 5. Examples; CHAPTER III: Tilting theory; 1. Grothendieck groups of triangulated categories; 2. The invariance property; 3. The Brenner-Butler Theorem; 4. Torsion theories; 5. Tilted algebras; 6. Partial tilting modules; 7. Concealed algebras CHAPTER IV: Piecewise hereditary algebras1. Piecewise hereditary algebras; 2. Cycles in mod kZ?; 3. The representation-finite case; 4. Iterated tilted algebras; 5. The general case; 6. The Dynkin case; 7. The affine case; CHAPTER V: Trivial extension algebras; 1. Preliminaries; 2. The representation-finite case; 3. The representation-infinite case; References; Index Triangulated categories. http://id.loc.gov/authorities/subjects/sh2010007133 Representations of algebras. http://id.loc.gov/authorities/subjects/sh85112938 Modules (Algebra) http://id.loc.gov/authorities/subjects/sh85086470 Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Catégories (Mathématiques) Représentations des algèbres. Modules (Algèbre) Catégories triangulées. MATHEMATICS Algebra Linear. bisacsh Categories (Mathematics) fast Modules (Algebra) fast Representations of algebras fast Triangulated categories fast Algebra gnd Darstellungstheorie gnd http://d-nb.info/gnd/4148816-7 Dimension n gnd http://d-nb.info/gnd/4309313-9 Kategorie Mathematik gnd http://d-nb.info/gnd/4129930-9 Triangulation gnd http://d-nb.info/gnd/4186017-2 Categorieën (wiskunde) gtt Associatieve ringen. gtt Algebra associativa. larpcal Algebra homologica. larpcal Représentations d'algèbres. ram Modules (algèbre) ram Catégories (mathématiques) ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh2010007133 http://id.loc.gov/authorities/subjects/sh85112938 http://id.loc.gov/authorities/subjects/sh85086470 http://id.loc.gov/authorities/subjects/sh85020992 http://d-nb.info/gnd/4148816-7 http://d-nb.info/gnd/4309313-9 http://d-nb.info/gnd/4129930-9 http://d-nb.info/gnd/4186017-2 |
| title | Triangulated categories in the representation theory of finite dimensional algebras / |
| title_auth | Triangulated categories in the representation theory of finite dimensional algebras / |
| title_exact_search | Triangulated categories in the representation theory of finite dimensional algebras / |
| title_full | Triangulated categories in the representation theory of finite dimensional algebras / Dieter Happel. |
| title_fullStr | Triangulated categories in the representation theory of finite dimensional algebras / Dieter Happel. |
| title_full_unstemmed | Triangulated categories in the representation theory of finite dimensional algebras / Dieter Happel. |
| title_short | Triangulated categories in the representation theory of finite dimensional algebras / |
| title_sort | triangulated categories in the representation theory of finite dimensional algebras |
| topic | Triangulated categories. http://id.loc.gov/authorities/subjects/sh2010007133 Representations of algebras. http://id.loc.gov/authorities/subjects/sh85112938 Modules (Algebra) http://id.loc.gov/authorities/subjects/sh85086470 Categories (Mathematics) http://id.loc.gov/authorities/subjects/sh85020992 Catégories (Mathématiques) Représentations des algèbres. Modules (Algèbre) Catégories triangulées. MATHEMATICS Algebra Linear. bisacsh Categories (Mathematics) fast Modules (Algebra) fast Representations of algebras fast Triangulated categories fast Algebra gnd Darstellungstheorie gnd http://d-nb.info/gnd/4148816-7 Dimension n gnd http://d-nb.info/gnd/4309313-9 Kategorie Mathematik gnd http://d-nb.info/gnd/4129930-9 Triangulation gnd http://d-nb.info/gnd/4186017-2 Categorieën (wiskunde) gtt Associatieve ringen. gtt Algebra associativa. larpcal Algebra homologica. larpcal Représentations d'algèbres. ram Modules (algèbre) ram Catégories (mathématiques) ram |
| topic_facet | Triangulated categories. Representations of algebras. Modules (Algebra) Categories (Mathematics) Catégories (Mathématiques) Représentations des algèbres. Modules (Algèbre) Catégories triangulées. MATHEMATICS Algebra Linear. Representations of algebras Triangulated categories Algebra Darstellungstheorie Dimension n Kategorie Mathematik Triangulation Categorieën (wiskunde) Associatieve ringen. Algebra associativa. Algebra homologica. Représentations d'algèbres. Modules (algèbre) Catégories (mathématiques) Triangulierte Kategorie. |
| work_keys_str_mv | AT happeldieter triangulatedcategoriesintherepresentationtheoryoffinitedimensionalalgebras |