Differential tensor algebras and their module categories:
This volume provides a systematic presentation of the theory of differential tensor algebras and their categories of modules. It involves reduction techniques which have proved to be very useful in the development of representation theory of finite dimensional algebras. The main results obtained wit...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2009
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| Schriftenreihe: | London Mathematical Society lecture note series
362 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | This volume provides a systematic presentation of the theory of differential tensor algebras and their categories of modules. It involves reduction techniques which have proved to be very useful in the development of representation theory of finite dimensional algebras. The main results obtained with these methods are presented in an elementary and self contained way. The authors provide a fresh point of view of well known facts on tame and wild differential tensor algebras, on tame and wild algebras, and on their modules. But there are also some new results and some new proofs. Their approach presents a formal alternative to the use of bocses (bimodules over categories with coalgebra structure) with underlying additive categories and pull-back reduction constructions. Professional mathematicians working in representation theory and related fields, and graduate students interested in homological algebra will find much of interest in this book |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (ix, 452 pages) |
| ISBN: | 9781139107105 |
| DOI: | 10.1017/CBO9781139107105 |
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| 100 | 1 | |a Bautista, R. |d 1943- |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Differential tensor algebras and their module categories |c R. Bautista, L. Salmerón, and R. Zuazua |
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 505 | 8 | |a T-algebras and differentials -- Dutalgebras and modules -- Bocses, ditalgebras and modules -- Layered ditalgebras -- Exact structures in A-mod -- Quotient ditalgebras -- Frames and roiter ditalgebras -- Product of ditalgebras -- Hom-tensor relations and dual basis -- Admissible modules -- Complete admissible modules -- Bimodule filtrations and triangular admissible modules -- Free bimodule filtrations and free datalgebras -- Examples and applications -- Passage from ditalgebras to finite-dimensional algebras -- Scalar extension and ditalgebras -- Bimodules -- Parametrizing bimodules and wildness -- Nested and seminested ditalgebras -- Critical diatalgebras -- Critical ditalgebras -- Reduction functors -- Reduction functions -- Modules over non-wild ditalgebras -- Tameness and wildness -- Modules over non-wild ditalgebras revisited -- Modules over non-wild algebras -- Absolute wildness -- Generic modules and tameness -- Varieties of modules over ditalgebras -- Ditalgebras of partially ordered sets -- Further examples of wild ditalgebras -- Answers to selected exercises | |
| 520 | |a This volume provides a systematic presentation of the theory of differential tensor algebras and their categories of modules. It involves reduction techniques which have proved to be very useful in the development of representation theory of finite dimensional algebras. The main results obtained with these methods are presented in an elementary and self contained way. The authors provide a fresh point of view of well known facts on tame and wild differential tensor algebras, on tame and wild algebras, and on their modules. But there are also some new results and some new proofs. Their approach presents a formal alternative to the use of bocses (bimodules over categories with coalgebra structure) with underlying additive categories and pull-back reduction constructions. Professional mathematicians working in representation theory and related fields, and graduate students interested in homological algebra will find much of interest in this book | ||
| 650 | 4 | |a Tensor algebra | |
| 650 | 4 | |a Representations of algebras | |
| 650 | 4 | |a Categories (Mathematics) | |
| 650 | 0 | 7 | |a Tensoralgebra |0 (DE-588)4505278-5 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Salmerón, L. |e Sonstige |4 oth | |
| 700 | 1 | |a Zuazua, R. |e Sonstige |4 oth | |
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Bautista, R. 1943- |
| author_facet | Bautista, R. 1943- |
| author_role | aut |
| author_sort | Bautista, R. 1943- |
| author_variant | r b rb |
| building | Verbundindex |
| bvnumber | BV043942096 |
| classification_rvk | SI 320 SK 220 SK 230 |
| collection | ZDB-20-CBO |
| contents | T-algebras and differentials -- Dutalgebras and modules -- Bocses, ditalgebras and modules -- Layered ditalgebras -- Exact structures in A-mod -- Quotient ditalgebras -- Frames and roiter ditalgebras -- Product of ditalgebras -- Hom-tensor relations and dual basis -- Admissible modules -- Complete admissible modules -- Bimodule filtrations and triangular admissible modules -- Free bimodule filtrations and free datalgebras -- Examples and applications -- Passage from ditalgebras to finite-dimensional algebras -- Scalar extension and ditalgebras -- Bimodules -- Parametrizing bimodules and wildness -- Nested and seminested ditalgebras -- Critical diatalgebras -- Critical ditalgebras -- Reduction functors -- Reduction functions -- Modules over non-wild ditalgebras -- Tameness and wildness -- Modules over non-wild ditalgebras revisited -- Modules over non-wild algebras -- Absolute wildness -- Generic modules and tameness -- Varieties of modules over ditalgebras -- Ditalgebras of partially ordered sets -- Further examples of wild ditalgebras -- Answers to selected exercises |
| ctrlnum | (ZDB-20-CBO)CR9781139107105 (OCoLC)967683535 (DE-599)BVBBV043942096 |
| dewey-full | 512/.57 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.57 |
| dewey-search | 512/.57 |
| dewey-sort | 3512 257 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139107105 |
| format | Electronic eBook |
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| id | DE-604.BV043942096 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9781139107105 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351066 |
| oclc_num | 967683535 |
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| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (ix, 452 pages) |
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| publishDate | 2009 |
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| publisher | Cambridge University Press |
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| spelling | Bautista, R. 1943- Verfasser aut Differential tensor algebras and their module categories R. Bautista, L. Salmerón, and R. Zuazua Differential Tensor Algebras & their Module Categories Cambridge Cambridge University Press 2009 1 online resource (ix, 452 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 362 Title from publisher's bibliographic system (viewed on 05 Oct 2015) T-algebras and differentials -- Dutalgebras and modules -- Bocses, ditalgebras and modules -- Layered ditalgebras -- Exact structures in A-mod -- Quotient ditalgebras -- Frames and roiter ditalgebras -- Product of ditalgebras -- Hom-tensor relations and dual basis -- Admissible modules -- Complete admissible modules -- Bimodule filtrations and triangular admissible modules -- Free bimodule filtrations and free datalgebras -- Examples and applications -- Passage from ditalgebras to finite-dimensional algebras -- Scalar extension and ditalgebras -- Bimodules -- Parametrizing bimodules and wildness -- Nested and seminested ditalgebras -- Critical diatalgebras -- Critical ditalgebras -- Reduction functors -- Reduction functions -- Modules over non-wild ditalgebras -- Tameness and wildness -- Modules over non-wild ditalgebras revisited -- Modules over non-wild algebras -- Absolute wildness -- Generic modules and tameness -- Varieties of modules over ditalgebras -- Ditalgebras of partially ordered sets -- Further examples of wild ditalgebras -- Answers to selected exercises This volume provides a systematic presentation of the theory of differential tensor algebras and their categories of modules. It involves reduction techniques which have proved to be very useful in the development of representation theory of finite dimensional algebras. The main results obtained with these methods are presented in an elementary and self contained way. The authors provide a fresh point of view of well known facts on tame and wild differential tensor algebras, on tame and wild algebras, and on their modules. But there are also some new results and some new proofs. Their approach presents a formal alternative to the use of bocses (bimodules over categories with coalgebra structure) with underlying additive categories and pull-back reduction constructions. Professional mathematicians working in representation theory and related fields, and graduate students interested in homological algebra will find much of interest in this book Tensor algebra Representations of algebras Categories (Mathematics) Tensoralgebra (DE-588)4505278-5 gnd rswk-swf Modulkategorie (DE-588)4170335-2 gnd rswk-swf Tensoralgebra (DE-588)4505278-5 s Modulkategorie (DE-588)4170335-2 s 1\p DE-604 Salmerón, L. Sonstige oth Zuazua, R. Sonstige oth Erscheint auch als Druckausgabe 978-0-521-75768-3 https://doi.org/10.1017/CBO9781139107105 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bautista, R. 1943- Differential tensor algebras and their module categories T-algebras and differentials -- Dutalgebras and modules -- Bocses, ditalgebras and modules -- Layered ditalgebras -- Exact structures in A-mod -- Quotient ditalgebras -- Frames and roiter ditalgebras -- Product of ditalgebras -- Hom-tensor relations and dual basis -- Admissible modules -- Complete admissible modules -- Bimodule filtrations and triangular admissible modules -- Free bimodule filtrations and free datalgebras -- Examples and applications -- Passage from ditalgebras to finite-dimensional algebras -- Scalar extension and ditalgebras -- Bimodules -- Parametrizing bimodules and wildness -- Nested and seminested ditalgebras -- Critical diatalgebras -- Critical ditalgebras -- Reduction functors -- Reduction functions -- Modules over non-wild ditalgebras -- Tameness and wildness -- Modules over non-wild ditalgebras revisited -- Modules over non-wild algebras -- Absolute wildness -- Generic modules and tameness -- Varieties of modules over ditalgebras -- Ditalgebras of partially ordered sets -- Further examples of wild ditalgebras -- Answers to selected exercises Tensor algebra Representations of algebras Categories (Mathematics) Tensoralgebra (DE-588)4505278-5 gnd Modulkategorie (DE-588)4170335-2 gnd |
| subject_GND | (DE-588)4505278-5 (DE-588)4170335-2 |
| title | Differential tensor algebras and their module categories |
| title_alt | Differential Tensor Algebras & their Module Categories |
| title_auth | Differential tensor algebras and their module categories |
| title_exact_search | Differential tensor algebras and their module categories |
| title_full | Differential tensor algebras and their module categories R. Bautista, L. Salmerón, and R. Zuazua |
| title_fullStr | Differential tensor algebras and their module categories R. Bautista, L. Salmerón, and R. Zuazua |
| title_full_unstemmed | Differential tensor algebras and their module categories R. Bautista, L. Salmerón, and R. Zuazua |
| title_short | Differential tensor algebras and their module categories |
| title_sort | differential tensor algebras and their module categories |
| topic | Tensor algebra Representations of algebras Categories (Mathematics) Tensoralgebra (DE-588)4505278-5 gnd Modulkategorie (DE-588)4170335-2 gnd |
| topic_facet | Tensor algebra Representations of algebras Categories (Mathematics) Tensoralgebra Modulkategorie |
| url | https://doi.org/10.1017/CBO9781139107105 |
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