Matrix Groups: An Introduction to Lie Group Theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London
Springer London
2002
|
| Schriftenreihe: | Springer Undergraduate Mathematics Series
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Aimed at advanced undergraduate and beginning graduate students, this book provides a first taste of the theory of Lie groups as an appetiser for a more substantial further course. Lie theoretic ideas lie at the heart of much of standard undergraduate linear algebra and exposure to them can inform or motivate the study of the latter. The main focus is on matrix groups, i.e., closed subgroups of real and complex general linear groups. The first part studies examples and describes the classical families of simply connected compact groups. The second part introduces the idea of a lie group and studies the associated notion of a homogeneous space using orbits of smooth actions. Throughout, the emphasis is on providing an approach that is accessible to readers equipped with a standard undergraduate toolkit of algebra and analysis. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully developed theory, preparing students for a more standard and abstract course in Lie theory and differential geometry |
| Beschreibung: | 1 Online-Ressource (XI, 330p. 16 illus) |
| ISBN: | 9781447101833 9781852334703 |
| ISSN: | 1615-2085 |
| DOI: | 10.1007/978-1-4471-0183-3 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4471-0183-3 |
| format | Electronic eBook |
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| isbn | 9781447101833 9781852334703 |
| issn | 1615-2085 |
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| spelling | Baker, Andrew Verfasser aut Matrix Groups An Introduction to Lie Group Theory by Andrew Baker London Springer London 2002 1 Online-Ressource (XI, 330p. 16 illus) txt rdacontent c rdamedia cr rdacarrier Springer Undergraduate Mathematics Series 1615-2085 Aimed at advanced undergraduate and beginning graduate students, this book provides a first taste of the theory of Lie groups as an appetiser for a more substantial further course. Lie theoretic ideas lie at the heart of much of standard undergraduate linear algebra and exposure to them can inform or motivate the study of the latter. The main focus is on matrix groups, i.e., closed subgroups of real and complex general linear groups. The first part studies examples and describes the classical families of simply connected compact groups. The second part introduces the idea of a lie group and studies the associated notion of a homogeneous space using orbits of smooth actions. Throughout, the emphasis is on providing an approach that is accessible to readers equipped with a standard undergraduate toolkit of algebra and analysis. Although the formal prerequisites are kept as low level as possible, the subject matter is sophisticated and contains many of the key themes of the fully developed theory, preparing students for a more standard and abstract course in Lie theory and differential geometry Mathematics Group theory Matrix theory Topological Groups Global differential geometry Topological Groups, Lie Groups Linear and Multilinear Algebras, Matrix Theory Differential Geometry Theoretical, Mathematical and Computational Physics Group Theory and Generalizations Mathematik Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Matrizengruppe (DE-588)4169127-1 gnd rswk-swf Matrizengruppe (DE-588)4169127-1 s 1\p DE-604 Lie-Gruppe (DE-588)4035695-4 s 2\p DE-604 https://doi.org/10.1007/978-1-4471-0183-3 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 |
| spellingShingle | Baker, Andrew Matrix Groups An Introduction to Lie Group Theory Mathematics Group theory Matrix theory Topological Groups Global differential geometry Topological Groups, Lie Groups Linear and Multilinear Algebras, Matrix Theory Differential Geometry Theoretical, Mathematical and Computational Physics Group Theory and Generalizations Mathematik Lie-Gruppe (DE-588)4035695-4 gnd Matrizengruppe (DE-588)4169127-1 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4169127-1 |
| title | Matrix Groups An Introduction to Lie Group Theory |
| title_auth | Matrix Groups An Introduction to Lie Group Theory |
| title_exact_search | Matrix Groups An Introduction to Lie Group Theory |
| title_full | Matrix Groups An Introduction to Lie Group Theory by Andrew Baker |
| title_fullStr | Matrix Groups An Introduction to Lie Group Theory by Andrew Baker |
| title_full_unstemmed | Matrix Groups An Introduction to Lie Group Theory by Andrew Baker |
| title_short | Matrix Groups |
| title_sort | matrix groups an introduction to lie group theory |
| title_sub | An Introduction to Lie Group Theory |
| topic | Mathematics Group theory Matrix theory Topological Groups Global differential geometry Topological Groups, Lie Groups Linear and Multilinear Algebras, Matrix Theory Differential Geometry Theoretical, Mathematical and Computational Physics Group Theory and Generalizations Mathematik Lie-Gruppe (DE-588)4035695-4 gnd Matrizengruppe (DE-588)4169127-1 gnd |
| topic_facet | Mathematics Group theory Matrix theory Topological Groups Global differential geometry Topological Groups, Lie Groups Linear and Multilinear Algebras, Matrix Theory Differential Geometry Theoretical, Mathematical and Computational Physics Group Theory and Generalizations Mathematik Lie-Gruppe Matrizengruppe |
| url | https://doi.org/10.1007/978-1-4471-0183-3 |
| work_keys_str_mv | AT bakerandrew matrixgroupsanintroductiontoliegrouptheory |