Elements of the representation theory of associative algebras: 1 Techniques of representation theory : Ibrahim Assem ; Universite de Sherbrooke ; Daniel Simson ; Nicolaus Copernicus University ; Andrzej Skowroński ; Nicolaus Copernicus University
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Pr.
2006
|
| Edition: | first published |
| Series: | London Mathematical Society student texts
65 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index. - Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | ix, 458 Seiten Diagramme |
| ISBN: | 052158423X 9780521584234 0521586313 9780521586313 |
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MARC
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| 250 | |a first published | ||
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Record in the Search Index
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Contents
0. Introduction page vii
1. Algebras and modules 1
1.1. Algebras 1
1.2. Modules 6
1.3. Semisimple modules and the radical of a module 13
1.4. Direct sum decompositions 18
1.5. Projective and injective modules 25
1.6. Basic algebras and embeddings of module categories 32
1.7. Exercises 38
II. Quivers and algebras 41
II. 1. Quivers and path algebras 41
11.2. Admissible ideals and quotients of the path algebra 53
11.3. The quiver of a finite dimensional algebra 59
11.4. Exercises 65
III. Representations and modules 69
111.1. Representations of bound quivers 69
111.2. The simple, projective, and injective modules 76
111.3. The dimension vector of a module and the Euler characteristic 86
111.4. Exercises 93
IV. Auslander—Reiten theory 97
IV. 1. Irreducible morphisms and almost split sequences 98
IV.2. The Auslander-Reiten translations 107
IV.3. The existence of almost split sequences 120
IV.4. The Auslander-Reiten quiver of an algebra 125
IV.5. The first Brauer-Thrall conjecture 138
IV.6. Functorial approach to almost split sequences 143
IV.7. Exercises 154
V. Nakayama algebras and representation—finite group
algebras 160
V.I. The Loewy series and the Loewy length of a module 160
V.2. Uniserial modules and right serial algebras 163
V.3. Nakayama algebras 168
V.4. Almost split sequences for Nakayama algebras 173
V.5. Representation-finite group algebras 175
V.6. Exercises 180
v
vi Contents
VI. Tilting theory 184
VI. 1. Torsion pairs 184
VI.2. Partial tilting modules and tilting modules 192
VI.3. The tilting theorem of Brenner and Butler 202
VI.4. Consequences of the tilting theorem 215
VI.5. Separating and splitting tilting modules 225
VI.6. Torsion pairs induced by tilting modules 232
VI.7. Exercises 238
VII. Representation—finite hereditary algebras 243
VII. 1. Hereditary algebras 243
VII.2. The Dynkin and Euclidean graphs 252
VII.3. Integral quadratic forms 259
VII.4. The quadratic form of a quiver 265
VII.5. Reflection functors and Gabriel's theorem 278
VII.6. Exercises 298
VIII. Tilted algebras 301
VIII. 1. Sections in translation quivers 301
VIII.2. Representation-infinite hereditary algebras 306
VIII.3. Tilted algebras 317
VIII.4. Projectives and injectives in the connecting component . . 326
VIII.5. The criterion of Liu and Skowroiiski 338
VIII.6. Exercises 350
IX. Directing modules and postprojective components 357
IX. 1. Directing modules 357
IX.2. Sincere directing modules 361
IX.3. Representation-directed algebras 366
IX.4. The separation condition 372
IX.5. Algebras such that all projectives are postprojective 379
IX.6. Gentle algebras and tilted algebras of type An 389
IX.7. Exercises 400
A. Appendix. Categories, functors, and homology 404
A.I. Categories 404
A.2. Functors 409
A.3. The radical of a category 420
A.4. Homological algebra 424
A.5. The group of extensions 431
A.6. Exercises 435
Bibliography 437
Index 451
List of symbols 457 |
| any_adam_object | 1 |
| author | Assem, Ibrahim Assem, Ibrahim Simson, Daniel 1942- Simson, Daniel 1942- Skowroński, Andrzej 1950-2020 Skowroński, Andrzej 1950-2020 |
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| author_facet | Assem, Ibrahim Assem, Ibrahim Simson, Daniel 1942- Simson, Daniel 1942- Skowroński, Andrzej 1950-2020 Skowroński, Andrzej 1950-2020 |
| author_role | aut aut aut aut aut aut |
| author_sort | Assem, Ibrahim |
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| building | Verbundindex |
| bvnumber | BV036513774 |
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| dewey-full | 512.46 |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512.46 |
| dewey-search | 512.46 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | first published |
| format | Book |
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| spelling | Assem, Ibrahim (DE-588)141208678 aut Elements of the representation theory of associative algebras 1 Techniques of representation theory : Ibrahim Assem ; Universite de Sherbrooke ; Daniel Simson ; Nicolaus Copernicus University ; Andrzej Skowroński ; Nicolaus Copernicus University Ibrahim Assem ; Daniel Simson ; Andrzej Skowroński first published Cambridge [u.a.] Cambridge Univ. Pr. 2006 ix, 458 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier London Mathematical Society student texts 65 London Mathematical Society student texts ... Includes bibliographical references and index. - Hier auch später erschienene, unveränderte Nachdrucke Assoziative Algebra (DE-588)4293934-3 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 s Assoziative Algebra (DE-588)4293934-3 s DE-604 Assem, Ibrahim Verfasser (DE-588)141208678 aut Simson, Daniel 1942- (DE-588)138525765 aut Simson, Daniel 1942- Verfasser (DE-588)138525765 aut Skowroński, Andrzej 1950-2020 (DE-588)141208694 aut Skowroński, Andrzej 1950-2020 Verfasser (DE-588)141208694 aut (DE-604)BV036513752 1 London Mathematical Society student texts 65 (DE-604)BV000841726 65 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020435930&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Assem, Ibrahim Assem, Ibrahim Simson, Daniel 1942- Simson, Daniel 1942- Skowroński, Andrzej 1950-2020 Skowroński, Andrzej 1950-2020 Elements of the representation theory of associative algebras London Mathematical Society student texts Assoziative Algebra (DE-588)4293934-3 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4293934-3 (DE-588)4148816-7 |
| title | Elements of the representation theory of associative algebras |
| title_auth | Elements of the representation theory of associative algebras |
| title_exact_search | Elements of the representation theory of associative algebras |
| title_full | Elements of the representation theory of associative algebras 1 Techniques of representation theory : Ibrahim Assem ; Universite de Sherbrooke ; Daniel Simson ; Nicolaus Copernicus University ; Andrzej Skowroński ; Nicolaus Copernicus University Ibrahim Assem ; Daniel Simson ; Andrzej Skowroński |
| title_fullStr | Elements of the representation theory of associative algebras 1 Techniques of representation theory : Ibrahim Assem ; Universite de Sherbrooke ; Daniel Simson ; Nicolaus Copernicus University ; Andrzej Skowroński ; Nicolaus Copernicus University Ibrahim Assem ; Daniel Simson ; Andrzej Skowroński |
| title_full_unstemmed | Elements of the representation theory of associative algebras 1 Techniques of representation theory : Ibrahim Assem ; Universite de Sherbrooke ; Daniel Simson ; Nicolaus Copernicus University ; Andrzej Skowroński ; Nicolaus Copernicus University Ibrahim Assem ; Daniel Simson ; Andrzej Skowroński |
| title_short | Elements of the representation theory of associative algebras |
| title_sort | elements of the representation theory of associative algebras techniques of representation theory ibrahim assem universite de sherbrooke daniel simson nicolaus copernicus university andrzej skowronski nicolaus copernicus university |
| topic | Assoziative Algebra (DE-588)4293934-3 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Assoziative Algebra Darstellungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020435930&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV036513752 (DE-604)BV000841726 |
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