Lie Groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2004
|
| Schriftenreihe: | Graduate Texts in Mathematics
225 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is intended for a one year graduate course on Lie groups and Lie algebras. The author proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and provides a carefully chosen range of material to give the student the bigger picture. For compact Lie groups, the Peter-Weyl theorem, conjugacy of maximal tori (two proofs), Weyl character formula and more are covered. The book continues with the study of complex analytic groups, then general noncompact Lie groups, including the Coxeter presentation of the Weyl group, the Iwasawa and Bruhat decompositions, Cartan decomposition, symmetric spaces, Cayley transforms, relative root systems, Satake diagrams, extended Dynkin diagrams and a survey of the ways Lie groups may be embedded in one another. The book culminates in a ''topics'' section giving depth to the student's understanding of representation theory, taking the Frobenius-Schur duality between the representation theory of the symmetric group and the unitary groups as a unifying theme, with many applications in diverse areas such as random matrix theory, minors of Toeplitz matrices, symmetric algebra decompositions, Gelfand pairs, Hecke algebras, representations of finite general linear groups and the cohomology of Grassmannians and flag varieties. Daniel Bump is Professor of Mathematics at Stanford University. His research is in automorphic forms, representation theory and number theory. He is a co-author of GNU Go, a computer program that plays the game of Go. His previous books include Automorphic Forms and Representations (Cambridge University Press 1997) and Algebraic Geometry (World Scientific 1998) |
| Beschreibung: | 1 Online-Ressource (XI, 454 p) |
| ISBN: | 9781475740943 9781441919373 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4757-4094-3 |
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Datensatz im Suchindex
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| author | Bump, Daniel |
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| dewey-full | 512.482 512.55 |
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| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-4094-3 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
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| institution | BVB |
| isbn | 9781475740943 9781441919373 |
| issn | 0072-5285 |
| language | English |
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| spelling | Bump, Daniel Verfasser aut Lie Groups by Daniel Bump New York, NY Springer New York 2004 1 Online-Ressource (XI, 454 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 225 0072-5285 This book is intended for a one year graduate course on Lie groups and Lie algebras. The author proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and provides a carefully chosen range of material to give the student the bigger picture. For compact Lie groups, the Peter-Weyl theorem, conjugacy of maximal tori (two proofs), Weyl character formula and more are covered. The book continues with the study of complex analytic groups, then general noncompact Lie groups, including the Coxeter presentation of the Weyl group, the Iwasawa and Bruhat decompositions, Cartan decomposition, symmetric spaces, Cayley transforms, relative root systems, Satake diagrams, extended Dynkin diagrams and a survey of the ways Lie groups may be embedded in one another. The book culminates in a ''topics'' section giving depth to the student's understanding of representation theory, taking the Frobenius-Schur duality between the representation theory of the symmetric group and the unitary groups as a unifying theme, with many applications in diverse areas such as random matrix theory, minors of Toeplitz matrices, symmetric algebra decompositions, Gelfand pairs, Hecke algebras, representations of finite general linear groups and the cohomology of Grassmannians and flag varieties. Daniel Bump is Professor of Mathematics at Stanford University. His research is in automorphic forms, representation theory and number theory. He is a co-author of GNU Go, a computer program that plays the game of Go. His previous books include Automorphic Forms and Representations (Cambridge University Press 1997) and Algebraic Geometry (World Scientific 1998) Mathematics Group theory Topological Groups Topological Groups, Lie Groups Group Theory and Generalizations Mathematik Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 s 1\p DE-604 Lie-Algebra (DE-588)4130355-6 s 2\p DE-604 https://doi.org/10.1007/978-1-4757-4094-3 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 | Bump, Daniel Lie Groups Mathematics Group theory Topological Groups Topological Groups, Lie Groups Group Theory and Generalizations Mathematik Lie-Gruppe (DE-588)4035695-4 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4130355-6 |
| title | Lie Groups |
| title_auth | Lie Groups |
| title_exact_search | Lie Groups |
| title_full | Lie Groups by Daniel Bump |
| title_fullStr | Lie Groups by Daniel Bump |
| title_full_unstemmed | Lie Groups by Daniel Bump |
| title_short | Lie Groups |
| title_sort | lie groups |
| topic | Mathematics Group theory Topological Groups Topological Groups, Lie Groups Group Theory and Generalizations Mathematik Lie-Gruppe (DE-588)4035695-4 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Mathematics Group theory Topological Groups Topological Groups, Lie Groups Group Theory and Generalizations Mathematik Lie-Gruppe Lie-Algebra |
| url | https://doi.org/10.1007/978-1-4757-4094-3 |
| work_keys_str_mv | AT bumpdaniel liegroups |