Lie groups, Lie algebras, and representations: an elementary introduction
Saved in:
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham ; Heidelberg ; New York ; Dordrecht ; London
Springer
[2015]
|
| Edition: | Second edition, corrected publication 2015 |
| Series: | Graduate texts in mathematics
222 |
| Subjects: | |
| Online Access: | Volltext Inhaltsverzeichnis Abstract |
| Physical Description: | 1 Online-Ressource (xiii, 449 Seiten) Illustrationen (teilweise farbig) |
| ISBN: | 9783319134673 |
| DOI: | 10.1007/978-3-319-13467-3 |
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Record in the Search Index
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|---|---|
| adam_text | LIE GROUPS, LIE ALGEBRAS, AND REPRESENTATIONS
/ HALL, BRIAN
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PART I: GENERAL THEORY.-MATRIX LIE GROUPS
THE MATRIX EXPONENTIAL
LIE ALGEBRAS
BASIC REPRESENTATION THEORY
THE BAKER–CAMPBELL–HAUSDORFF FORMULA AND ITS CONSEQUENCES
PART II: SEMISIMPLE LIE ALGEBRAS
THE REPRESENTATIONS OF SL(3;C).-SEMISIMPLE LIE ALGEBRAS.-ROOT SYSTEMS
REPRESENTATIONS OF SEMISIMPLE LIE ALGEBRAS
FURTHER PROPERTIES OF THE REPRESENTATIONS
PART III: COMPACT LIE GROUPS
COMPACT LIE GROUPS AND MAXIMAL TORI
THE COMPACT GROUP APPROACH TO REPRESENTATION THEORY
FUNDAMENTAL GROUPS OF COMPACT LIE GROUPS
APPENDICES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
LIE GROUPS, LIE ALGEBRAS, AND REPRESENTATIONS
/ HALL, BRIAN
: 2015
ABSTRACT / INHALTSTEXT
THIS TEXTBOOK TREATS LIE GROUPS, LIE ALGEBRAS AND THEIR REPRESENTATIONS
IN AN ELEMENTARY BUT FULLY RIGOROUS FASHION REQUIRING MINIMAL
PREREQUISITES. IN PARTICULAR, THE THEORY OF MATRIX LIE GROUPS AND THEIR
LIE ALGEBRAS IS DEVELOPED USING ONLY LINEAR ALGEBRA, AND MORE MOTIVATION
AND INTUITION FOR PROOFS IS PROVIDED THAN IN MOST CLASSIC TEXTS ON THE
SUBJECT.IN ADDITION TO ITS ACCESSIBLE TREATMENT OF THE BASIC THEORY OF
LIE GROUPS AND LIE ALGEBRAS, THE BOOK IS ALSO NOTEWORTHY FOR INCLUDING:
A TREATMENT OF THE BAKER–CAMPBELL–HAUSDORFF FORMULA AND ITS USE IN
PLACE OF THE FROBENIUS THEOREM TO ESTABLISH DEEPER RESULTS ABOUT THE
RELATIONSHIP BETWEEN LIE GROUPS AND LIE ALGEBRAS MOTIVATION FOR THE
MACHINERY OF ROOTS, WEIGHTS AND THE WEYL GROUP VIA A CONCRETE AND
DETAILED EXPOSITION OF THE REPRESENTATION THEORY OF SL(3;C) AN
UNCONVENTIONAL DEFINITION OF SEMISIMPLICITY THAT ALLOWS FOR A RAPID
DEVELOPMENT OF THE STRUCTURE THEORY OF SEMISIMPLE LIE ALGEBRAS A
SELF-CONTAINED CONSTRUCTION OF THE REPRESENTATIONS OF COMPACT GROUPS,
INDEPENDENT OF LIE-ALGEBRAIC ARGUMENTS THE SECOND EDITION OF LIE GROUPS,
LIE ALGEBRAS, AND REPRESENTATIONS CONTAINS MANY SUBSTANTIAL IMPROVEMENTS
AND ADDITIONS,AMONG THEM: AN ENTIRELY NEW PART DEVOTED TO THE STRUCTURE
AND REPRESENTATION THEORY OF COMPACT LIE GROUPS; A COMPLETE DERIVATION
OF THE MAIN PROPERTIES OF ROOT SYSTEMS; THE CONSTRUCTION OF
FINITE-DIMENSIONAL REPRESENTATIONS OF SEMISIMPLE LIE ALGEBRAS HAS BEEN
ELABORATED; A TREATMENT OF UNIVERSAL ENVELOPING ALGEBRAS, INCLUDING A
PROOF OF THE POINCARE–BIRKHOFF–WITT THEOREM AND THE EXISTENCE OF
VERMA MODULES; COMPLETE PROOFS OF THE WEYL CHARACTER FORMULA, THE WEYL
DIMENSION FORMULA AND THE KOSTANT MULTIPLICITY FORMULA. REVIEW OF THE
FIRST EDITION: “THIS IS AN EXCELLENT BOOK. IT DESERVES TO, AND
UNDOUBTEDLY WILL, BECOME THE STANDARD TEXT FOR EARLY GRADUATE COURSES IN
LIE GROUP THEORY ... AN IMPORTANT ADDITION TO THE TEXTBOOK LITERATURE
... IT IS HIGHLY RECOMMENDED.” — THE MATHEMATICAL GAZETTE
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-13467-3 |
| edition | Second edition, corrected publication 2015 |
| format | Electronic eBook |
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| id | DE-604.BV042592090 |
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| indexdate | 2024-07-10T07:05:25Z |
| institution | BVB |
| isbn | 9783319134673 |
| language | English |
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| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Hall, Brian C. Verfasser (DE-588)1038321050 aut Lie groups, Lie algebras, and representations an elementary introduction Brian Hall Second edition, corrected publication 2015 Cham ; Heidelberg ; New York ; Dordrecht ; London Springer [2015] © 2015 1 Online-Ressource (xiii, 449 Seiten) Illustrationen (teilweise farbig) txt rdacontent c rdamedia cr rdacarrier Graduate texts in mathematics 222 Mathematics Algebra Topological Groups Cell aggregation / Mathematics Topological Groups, Lie Groups Non-associative Rings and Algebras Manifolds and Cell Complexes (incl. Diff.Topology) Lie-Gruppe - Lie-Algebra - Darstellungstheorie Mathematik Lie algebras Lie groups Representations of algebras Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 s Lie-Algebra (DE-588)4130355-6 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Erscheint auch als Druck-Ausgabe, Hardcover 978-3-319-13466-6 Erscheint auch als Druck-Ausgabe, Paperback 978-3-319-37433-8 Graduate texts in mathematics 222 (DE-604)BV035421258 222 https://doi.org/10.1007/978-3-319-13467-3 Verlag URL des Erstveröffentlichers Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028025302&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028025302&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Hall, Brian C. Lie groups, Lie algebras, and representations an elementary introduction Graduate texts in mathematics Mathematics Algebra Topological Groups Cell aggregation / Mathematics Topological Groups, Lie Groups Non-associative Rings and Algebras Manifolds and Cell Complexes (incl. Diff.Topology) Lie-Gruppe - Lie-Algebra - Darstellungstheorie Mathematik Lie algebras Lie groups Representations of algebras Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd Lie-Algebra (DE-588)4130355-6 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4130355-6 (DE-588)4035695-4 |
| title | Lie groups, Lie algebras, and representations an elementary introduction |
| title_auth | Lie groups, Lie algebras, and representations an elementary introduction |
| title_exact_search | Lie groups, Lie algebras, and representations an elementary introduction |
| title_full | Lie groups, Lie algebras, and representations an elementary introduction Brian Hall |
| title_fullStr | Lie groups, Lie algebras, and representations an elementary introduction Brian Hall |
| title_full_unstemmed | Lie groups, Lie algebras, and representations an elementary introduction Brian Hall |
| title_short | Lie groups, Lie algebras, and representations |
| title_sort | lie groups lie algebras and representations an elementary introduction |
| title_sub | an elementary introduction |
| topic | Mathematics Algebra Topological Groups Cell aggregation / Mathematics Topological Groups, Lie Groups Non-associative Rings and Algebras Manifolds and Cell Complexes (incl. Diff.Topology) Lie-Gruppe - Lie-Algebra - Darstellungstheorie Mathematik Lie algebras Lie groups Representations of algebras Representations of groups Darstellungstheorie (DE-588)4148816-7 gnd Lie-Algebra (DE-588)4130355-6 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| topic_facet | Mathematics Algebra Topological Groups Cell aggregation / Mathematics Topological Groups, Lie Groups Non-associative Rings and Algebras Manifolds and Cell Complexes (incl. Diff.Topology) Lie-Gruppe - Lie-Algebra - Darstellungstheorie Mathematik Lie algebras Lie groups Representations of algebras Representations of groups Darstellungstheorie Lie-Algebra Lie-Gruppe |
| url | https://doi.org/10.1007/978-3-319-13467-3 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028025302&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028025302&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035421258 |
| work_keys_str_mv | AT hallbrianc liegroupsliealgebrasandrepresentationsanelementaryintroduction |