Homological theory of representations:
Modern developments in representation theory rely heavily on homological methods. This book for advanced graduate students and researchers introduces these methods from their foundations up and discusses several landmark results that illustrate their power and beauty. Categorical foundations include...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2022
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
195 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Modern developments in representation theory rely heavily on homological methods. This book for advanced graduate students and researchers introduces these methods from their foundations up and discusses several landmark results that illustrate their power and beauty. Categorical foundations include abelian and derived categories, with an emphasis on localisation, spectra, and purity. The representation theoretic focus is on module categories of Artin algebras, with discussions of the representation theory of finite groups and finite quivers. Also covered are Gorenstein and quasi-hereditary algebras, including Schur algebras, which model polynomial representations of general linear groups, and the Morita theory of derived categories via tilting objects. The final part is devoted to a systematic introduction to the theory of purity for locally finitely presented categories, covering pure-injectives, definable subcategories, and Ziegler spectra. With its clear, detailed exposition of important topics in modern representation theory, many of which were unavailable in one volume until now, it deserves a place in every representation theorist's library |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 12 Nov 2021) |
| Beschreibung: | 1 Online-Ressource (xxxiv, 482 Seiten) |
| ISBN: | 9781108979108 |
| DOI: | 10.1017/9781108979108 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV047655304 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 211228s2021 |||| o||u| ||||||eng d | ||
| 020 | |a 9781108979108 |c Online |9 978-1-108-97910-8 | ||
| 024 | 7 | |a 10.1017/9781108979108 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9781108979108 | ||
| 035 | |a (OCoLC)1291619393 | ||
| 035 | |a (DE-599)BVBBV047655304 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 | ||
| 082 | 0 | |a 512.55 | |
| 084 | |a SK 260 |0 (DE-625)143227: |2 rvk | ||
| 084 | |a SK 320 |0 (DE-625)143231: |2 rvk | ||
| 100 | 1 | |a Krause, Henning |d 1962- |0 (DE-588)1126055913 |4 aut | |
| 245 | 1 | 0 | |a Homological theory of representations |c Henning Krause |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2022 | |
| 300 | |a 1 Online-Ressource (xxxiv, 482 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Cambridge studies in advanced mathematics | |
| 490 | 0 | |a 195 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 12 Nov 2021) | ||
| 520 | |a Modern developments in representation theory rely heavily on homological methods. This book for advanced graduate students and researchers introduces these methods from their foundations up and discusses several landmark results that illustrate their power and beauty. Categorical foundations include abelian and derived categories, with an emphasis on localisation, spectra, and purity. The representation theoretic focus is on module categories of Artin algebras, with discussions of the representation theory of finite groups and finite quivers. Also covered are Gorenstein and quasi-hereditary algebras, including Schur algebras, which model polynomial representations of general linear groups, and the Morita theory of derived categories via tilting objects. The final part is devoted to a systematic introduction to the theory of purity for locally finitely presented categories, covering pure-injectives, definable subcategories, and Ziegler spectra. With its clear, detailed exposition of important topics in modern representation theory, many of which were unavailable in one volume until now, it deserves a place in every representation theorist's library | ||
| 650 | 4 | |a Algebra, Homological | |
| 650 | 4 | |a Representations of algebras | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-1-108-83889-4 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/9781108979108 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-033040245 | ||
| 966 | e | |u https://doi.org/10.1017/9781108979108 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/9781108979108 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804183122469715968 |
|---|---|
| adam_txt | |
| any_adam_object | |
| any_adam_object_boolean | |
| author | Krause, Henning 1962- |
| author_GND | (DE-588)1126055913 |
| author_facet | Krause, Henning 1962- |
| author_role | aut |
| author_sort | Krause, Henning 1962- |
| author_variant | h k hk |
| building | Verbundindex |
| bvnumber | BV047655304 |
| classification_rvk | SK 260 SK 320 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9781108979108 (OCoLC)1291619393 (DE-599)BVBBV047655304 |
| dewey-full | 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 |
| dewey-search | 512.55 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1017/9781108979108 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02815nmm a2200445zc 4500</leader><controlfield tag="001">BV047655304</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">211228s2021 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781108979108</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-108-97910-8</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/9781108979108</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9781108979108</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1291619393</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV047655304</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.55</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 260</subfield><subfield code="0">(DE-625)143227:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 320</subfield><subfield code="0">(DE-625)143231:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Krause, Henning</subfield><subfield code="d">1962-</subfield><subfield code="0">(DE-588)1126055913</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Homological theory of representations</subfield><subfield code="c">Henning Krause</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">2022</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xxxiv, 482 Seiten)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Cambridge studies in advanced mathematics</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">195</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 12 Nov 2021)</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Modern developments in representation theory rely heavily on homological methods. This book for advanced graduate students and researchers introduces these methods from their foundations up and discusses several landmark results that illustrate their power and beauty. Categorical foundations include abelian and derived categories, with an emphasis on localisation, spectra, and purity. The representation theoretic focus is on module categories of Artin algebras, with discussions of the representation theory of finite groups and finite quivers. Also covered are Gorenstein and quasi-hereditary algebras, including Schur algebras, which model polynomial representations of general linear groups, and the Morita theory of derived categories via tilting objects. The final part is devoted to a systematic introduction to the theory of purity for locally finitely presented categories, covering pure-injectives, definable subcategories, and Ziegler spectra. With its clear, detailed exposition of important topics in modern representation theory, many of which were unavailable in one volume until now, it deserves a place in every representation theorist's library</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebra, Homological</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Representations of algebras</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-1-108-83889-4</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/9781108979108</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-033040245</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/9781108979108</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/9781108979108</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV047655304 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:50:57Z |
| indexdate | 2024-07-10T09:18:25Z |
| institution | BVB |
| isbn | 9781108979108 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033040245 |
| oclc_num | 1291619393 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 Online-Ressource (xxxiv, 482 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2022 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge studies in advanced mathematics 195 |
| spelling | Krause, Henning 1962- (DE-588)1126055913 aut Homological theory of representations Henning Krause Cambridge Cambridge University Press 2022 1 Online-Ressource (xxxiv, 482 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 195 Title from publisher's bibliographic system (viewed on 12 Nov 2021) Modern developments in representation theory rely heavily on homological methods. This book for advanced graduate students and researchers introduces these methods from their foundations up and discusses several landmark results that illustrate their power and beauty. Categorical foundations include abelian and derived categories, with an emphasis on localisation, spectra, and purity. The representation theoretic focus is on module categories of Artin algebras, with discussions of the representation theory of finite groups and finite quivers. Also covered are Gorenstein and quasi-hereditary algebras, including Schur algebras, which model polynomial representations of general linear groups, and the Morita theory of derived categories via tilting objects. The final part is devoted to a systematic introduction to the theory of purity for locally finitely presented categories, covering pure-injectives, definable subcategories, and Ziegler spectra. With its clear, detailed exposition of important topics in modern representation theory, many of which were unavailable in one volume until now, it deserves a place in every representation theorist's library Algebra, Homological Representations of algebras Erscheint auch als Druck-Ausgabe 978-1-108-83889-4 https://doi.org/10.1017/9781108979108 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Krause, Henning 1962- Homological theory of representations Algebra, Homological Representations of algebras |
| title | Homological theory of representations |
| title_auth | Homological theory of representations |
| title_exact_search | Homological theory of representations |
| title_exact_search_txtP | Homological theory of representations |
| title_full | Homological theory of representations Henning Krause |
| title_fullStr | Homological theory of representations Henning Krause |
| title_full_unstemmed | Homological theory of representations Henning Krause |
| title_short | Homological theory of representations |
| title_sort | homological theory of representations |
| topic | Algebra, Homological Representations of algebras |
| topic_facet | Algebra, Homological Representations of algebras |
| url | https://doi.org/10.1017/9781108979108 |
| work_keys_str_mv | AT krausehenning homologicaltheoryofrepresentations |