Two-dimensional tame and maximal orders of finite representation type:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
1989
|
| Series: | American Mathematical Society: Memoirs of the American Mathematical Society
408 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 80, Number 408 (fourth of 5 numbers) |
| Physical Description: | VIII, 72 S. |
| ISBN: | 0821824694 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804120846574288896 |
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| adam_text | TABLE OF CONTENTS
INTRODUCTION v
1. TAME AND MAXIMAL ORDERS AND THEIR
GROTHENDIECK GROUPS 1
1.1 Orders 1
1.2 Reflexive Morita equivalence 2
1.3 Grothendieck group of tame and maximal orders 7
2. THE ASSOCIATED GRADED ORDERS 12
2.1 The shape of the Auslander Reiten quivers 13
2.2 The associated graded algebras 15
2.3 The isomorphism classes of the path algebras with
quadratic relations 20
2.4 Properties of the path algebras with quadratic relations
and their completions 26
2.5 The classification for gr A 31
2.6 k[[xlvx2]] algebras 33
2.7 General comments on existence of almost split
sequences 34
3. THE LATTICE OF OVERLYING ORDERS 36
3.1 The Grothendieck group of a translation quiver 36
3.2 Admissible sets and zero sets 39
3.3 Zero sets of tame orders 41
3.4 When are A and End. (M) reflexive Morita equivalent? 44
3.5 AR quivers for overorders 45
3.6 Relationship between KJmodj A) and K0(mod A) 47
4. MAXIMAL ORDERS OF FINITE REPRESENTATION TYPE 49
4.1 The method _ 49
4.2 The universal covering of T is ZDn 52
4.3 The universal covering is ZEj 54
4.4 The universal covering is ZA?° 57
4.5 Noncommutative maximal orders 59
5. PASSING FROM THE GRADED TO THE COMPLETE CASE 62
5.1 Graded methods 63
5.2 Reflexive Galois extensions 64
5.3 Interpretation as skew group ring 66
REFERENCES 70
|
| any_adam_object | 1 |
| author | Reiten, Idun 1942- Van den Bergh, Michel 1960- |
| author_GND | (DE-588)108418413 (DE-588)134166949 |
| author_facet | Reiten, Idun 1942- Van den Bergh, Michel 1960- |
| author_role | aut aut |
| author_sort | Reiten, Idun 1942- |
| author_variant | i r ir d b m v dbm dbmv |
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| bvnumber | BV006575940 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
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| callnumber-subject | QA - Mathematics |
| classification_tum | MAT 160f |
| ctrlnum | (OCoLC)19921687 (DE-599)BVBBV006575940 |
| dewey-full | 512/.24 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 510 - Mathematics |
| dewey-raw | 512/.24 510 |
| dewey-search | 512/.24 510 |
| dewey-sort | 3512 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV006575940 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:48:35Z |
| institution | BVB |
| isbn | 0821824694 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004195762 |
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| physical | VIII, 72 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | American Mathematical Society: Memoirs of the American Mathematical Society |
| series2 | American Mathematical Society: Memoirs of the American Mathematical Society |
| spelling | Reiten, Idun 1942- Verfasser (DE-588)108418413 aut Two-dimensional tame and maximal orders of finite representation type Idun Reiten and Michel van den Bergh Providence, RI American Math. Soc. 1989 VIII, 72 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Memoirs of the American Mathematical Society 408 Volume 80, Number 408 (fourth of 5 numbers) Algebra Associativa larpcal Teoria Dos Grupos larpcal Associative algebras Grothendieck groups Representations of algebras Maximalordnung (DE-588)4169161-1 gnd rswk-swf Grothendieck-Gruppe (DE-588)4158321-8 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Darstellung (DE-588)4200624-7 gnd rswk-swf Assoziative Algebra (DE-588)4293934-3 gnd rswk-swf Zahme Ordnung (DE-588)4222898-0 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Grothendieck-Gruppe (DE-588)4158321-8 s DE-604 Assoziative Algebra (DE-588)4293934-3 s Darstellung (DE-588)4200624-7 s Zahme Ordnung (DE-588)4222898-0 s Darstellungstheorie (DE-588)4148816-7 s Maximalordnung (DE-588)4169161-1 s Darstellung Mathematik (DE-588)4128289-9 s Van den Bergh, Michel 1960- Verfasser (DE-588)134166949 aut American Mathematical Society: Memoirs of the American Mathematical Society 408 (DE-604)BV008000141 408 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004195762&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reiten, Idun 1942- Van den Bergh, Michel 1960- Two-dimensional tame and maximal orders of finite representation type American Mathematical Society: Memoirs of the American Mathematical Society Algebra Associativa larpcal Teoria Dos Grupos larpcal Associative algebras Grothendieck groups Representations of algebras Maximalordnung (DE-588)4169161-1 gnd Grothendieck-Gruppe (DE-588)4158321-8 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Darstellung (DE-588)4200624-7 gnd Assoziative Algebra (DE-588)4293934-3 gnd Zahme Ordnung (DE-588)4222898-0 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4169161-1 (DE-588)4158321-8 (DE-588)4128289-9 (DE-588)4200624-7 (DE-588)4293934-3 (DE-588)4222898-0 (DE-588)4148816-7 |
| title | Two-dimensional tame and maximal orders of finite representation type |
| title_auth | Two-dimensional tame and maximal orders of finite representation type |
| title_exact_search | Two-dimensional tame and maximal orders of finite representation type |
| title_full | Two-dimensional tame and maximal orders of finite representation type Idun Reiten and Michel van den Bergh |
| title_fullStr | Two-dimensional tame and maximal orders of finite representation type Idun Reiten and Michel van den Bergh |
| title_full_unstemmed | Two-dimensional tame and maximal orders of finite representation type Idun Reiten and Michel van den Bergh |
| title_short | Two-dimensional tame and maximal orders of finite representation type |
| title_sort | two dimensional tame and maximal orders of finite representation type |
| topic | Algebra Associativa larpcal Teoria Dos Grupos larpcal Associative algebras Grothendieck groups Representations of algebras Maximalordnung (DE-588)4169161-1 gnd Grothendieck-Gruppe (DE-588)4158321-8 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Darstellung (DE-588)4200624-7 gnd Assoziative Algebra (DE-588)4293934-3 gnd Zahme Ordnung (DE-588)4222898-0 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Algebra Associativa Teoria Dos Grupos Associative algebras Grothendieck groups Representations of algebras Maximalordnung Grothendieck-Gruppe Darstellung Mathematik Darstellung Assoziative Algebra Zahme Ordnung Darstellungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004195762&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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