Representation Theory: A First Course
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2004
|
| Schriftenreihe: | Graduate Texts in Mathematics, Readings in Mathematics
129 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific |
| Beschreibung: | 1 Online-Ressource (XV, 551 p) |
| ISBN: | 9781461209799 9783540005391 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-0979-9 |
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| 500 | |a The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific | ||
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Datensatz im Suchindex
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| author | Fulton, William |
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| dewey-full | 512.55 512.482 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 512.482 |
| dewey-search | 512.55 512.482 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0979-9 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:05Z |
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| isbn | 9781461209799 9783540005391 |
| issn | 0072-5285 |
| language | English |
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| spelling | Fulton, William Verfasser aut Representation Theory A First Course by William Fulton, Joe Harris New York, NY Springer New York 2004 1 Online-Ressource (XV, 551 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics, Readings in Mathematics 129 0072-5285 The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s Darstellungstheorie (DE-588)4148816-7 s 1\p DE-604 Lie-Gruppe (DE-588)4035695-4 s 2\p DE-604 Darstellung Mathematik (DE-588)4128289-9 s 3\p DE-604 4\p DE-604 Gruppe Mathematik (DE-588)4022379-6 s 5\p DE-604 Harris, Joe Sonstige oth https://doi.org/10.1007/978-1-4612-0979-9 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 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fulton, William Representation Theory A First Course Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Lie-Algebra (DE-588)4130355-6 gnd Gruppe Mathematik (DE-588)4022379-6 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Lie-Gruppe (DE-588)4035695-4 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4130355-6 (DE-588)4022379-6 (DE-588)4128289-9 (DE-588)4035695-4 (DE-588)4148816-7 |
| title | Representation Theory A First Course |
| title_auth | Representation Theory A First Course |
| title_exact_search | Representation Theory A First Course |
| title_full | Representation Theory A First Course by William Fulton, Joe Harris |
| title_fullStr | Representation Theory A First Course by William Fulton, Joe Harris |
| title_full_unstemmed | Representation Theory A First Course by William Fulton, Joe Harris |
| title_short | Representation Theory |
| title_sort | representation theory a first course |
| title_sub | A First Course |
| topic | Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Lie-Algebra (DE-588)4130355-6 gnd Gruppe Mathematik (DE-588)4022379-6 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Lie-Gruppe (DE-588)4035695-4 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Mathematics Topological Groups Topological Groups, Lie Groups Mathematik Lie-Algebra Gruppe Mathematik Darstellung Mathematik Lie-Gruppe Darstellungstheorie |
| url | https://doi.org/10.1007/978-1-4612-0979-9 |
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