Induced modules over group algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
North-Holland
1990
|
| Schriftenreihe: | North-Holland mathematics studies
161 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In 1898 Frobenius discovered a construction which, in present terminology, associates with every module of a subgroup the induced module of a group. This construction proved to be of fundamental importance and is one of the basic tools in the entire theory of group representations. This monograph is designed for research mathematicians and advanced graduate students and gives a picture of the general theory of induced modules as it exists at present. Much of the material has until now been available only in research articles. The approach is not intended to be encyclopedic, rather each topic is considered in sufficient depth that the reader may obtain a clear idea of the major results in the area. After establishing algebraic preliminaries, the general facts about induced modules are provided, as well as some of their formal properties, annihilators and applications. The remaining chapters include detailed information on the process of induction from normal subgroups, projective summands of induced modules, some basic results of the Green theory with refinements and extensions, simple induction and restriction pairs and permutation modules. The final chapter is based exclusively on the work of Weiss, presenting a number of applications to the isomorphism problem for group rings Includes bibliographical references (p. 499-510) and index |
| Beschreibung: | 1 Online-Ressource (xi, 520 p.) |
| ISBN: | 9780444884145 0444884149 |
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| 490 | 0 | |a North-Holland mathematics studies |v 161 | |
| 500 | |a In 1898 Frobenius discovered a construction which, in present terminology, associates with every module of a subgroup the induced module of a group. This construction proved to be of fundamental importance and is one of the basic tools in the entire theory of group representations. This monograph is designed for research mathematicians and advanced graduate students and gives a picture of the general theory of induced modules as it exists at present. Much of the material has until now been available only in research articles. The approach is not intended to be encyclopedic, rather each topic is considered in sufficient depth that the reader may obtain a clear idea of the major results in the area. After establishing algebraic preliminaries, the general facts about induced modules are provided, as well as some of their formal properties, annihilators and applications. The remaining chapters include detailed information on the process of induction from normal subgroups, projective summands of induced modules, some basic results of the Green theory with refinements and extensions, simple induction and restriction pairs and permutation modules. The final chapter is based exclusively on the work of Weiss, presenting a number of applications to the isomorphism problem for group rings | ||
| 500 | |a Includes bibliographical references (p. 499-510) and index | ||
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Datensatz im Suchindex
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| author | Karpilovsky, Gregory |
| author_facet | Karpilovsky, Gregory |
| author_role | aut |
| author_sort | Karpilovsky, Gregory |
| author_variant | g k gk |
| building | Verbundindex |
| bvnumber | BV042317844 |
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| dewey-full | 512/.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.24 |
| dewey-search | 512/.24 |
| dewey-sort | 3512 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:18:17Z |
| institution | BVB |
| isbn | 9780444884145 0444884149 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027754835 |
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| physical | 1 Online-Ressource (xi, 520 p.) |
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| publishDate | 1990 |
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| publisher | North-Holland |
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| series2 | North-Holland mathematics studies |
| spelling | Karpilovsky, Gregory Verfasser aut Induced modules over group algebras Gregory Karpilovsky Amsterdam North-Holland 1990 1 Online-Ressource (xi, 520 p.) txt rdacontent c rdamedia cr rdacarrier North-Holland mathematics studies 161 In 1898 Frobenius discovered a construction which, in present terminology, associates with every module of a subgroup the induced module of a group. This construction proved to be of fundamental importance and is one of the basic tools in the entire theory of group representations. This monograph is designed for research mathematicians and advanced graduate students and gives a picture of the general theory of induced modules as it exists at present. Much of the material has until now been available only in research articles. The approach is not intended to be encyclopedic, rather each topic is considered in sufficient depth that the reader may obtain a clear idea of the major results in the area. After establishing algebraic preliminaries, the general facts about induced modules are provided, as well as some of their formal properties, annihilators and applications. The remaining chapters include detailed information on the process of induction from normal subgroups, projective summands of induced modules, some basic results of the Green theory with refinements and extensions, simple induction and restriction pairs and permutation modules. The final chapter is based exclusively on the work of Weiss, presenting a number of applications to the isomorphism problem for group rings Includes bibliographical references (p. 499-510) and index Algèbres de groupes ram Modules (Algèbre) ram Group algebras fast Modules (Algebra) fast Group algebras Modules (Algebra) Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Modul (DE-588)4129770-2 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Gruppenring (DE-588)4158469-7 gnd rswk-swf Modul (DE-588)4129770-2 s Gruppenring (DE-588)4158469-7 s 1\p DE-604 Gruppe Mathematik (DE-588)4022379-6 s 2\p DE-604 Algebra (DE-588)4001156-2 s 3\p DE-604 http://www.sciencedirect.com/science/book/9780444884145 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Karpilovsky, Gregory Induced modules over group algebras Algèbres de groupes ram Modules (Algèbre) ram Group algebras fast Modules (Algebra) fast Group algebras Modules (Algebra) Gruppe Mathematik (DE-588)4022379-6 gnd Modul (DE-588)4129770-2 gnd Algebra (DE-588)4001156-2 gnd Gruppenring (DE-588)4158469-7 gnd |
| subject_GND | (DE-588)4022379-6 (DE-588)4129770-2 (DE-588)4001156-2 (DE-588)4158469-7 |
| title | Induced modules over group algebras |
| title_auth | Induced modules over group algebras |
| title_exact_search | Induced modules over group algebras |
| title_full | Induced modules over group algebras Gregory Karpilovsky |
| title_fullStr | Induced modules over group algebras Gregory Karpilovsky |
| title_full_unstemmed | Induced modules over group algebras Gregory Karpilovsky |
| title_short | Induced modules over group algebras |
| title_sort | induced modules over group algebras |
| topic | Algèbres de groupes ram Modules (Algèbre) ram Group algebras fast Modules (Algebra) fast Group algebras Modules (Algebra) Gruppe Mathematik (DE-588)4022379-6 gnd Modul (DE-588)4129770-2 gnd Algebra (DE-588)4001156-2 gnd Gruppenring (DE-588)4158469-7 gnd |
| topic_facet | Algèbres de groupes Modules (Algèbre) Group algebras Modules (Algebra) Gruppe Mathematik Modul Algebra Gruppenring |
| url | http://www.sciencedirect.com/science/book/9780444884145 |
| work_keys_str_mv | AT karpilovskygregory inducedmodulesovergroupalgebras |