Potential theory and geometry on Lie groups:
This book provides a complete and reasonably self-contained account of a new classification of connected Lie groups into two classes. The first part describes the use of tools from potential theory to establish the classification and to show that the analytic and algebraic approaches to the classifi...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, United Kingdom ; New York, NY, USA ; Port Melbourne, VIC, Australia ; New Delhi, India ; Singapore
Cambridge University Press
2020
|
| Schriftenreihe: | New mathematical monographs
38 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 TUM01 TUM02 UBA01 Volltext |
| Zusammenfassung: | This book provides a complete and reasonably self-contained account of a new classification of connected Lie groups into two classes. The first part describes the use of tools from potential theory to establish the classification and to show that the analytic and algebraic approaches to the classification are equivalent. Part II covers geometric theory of the same classification and a proof that it is equivalent to the algebraic approach. Part III is a new approach to the geometric classification that requires more advanced geometric technology, namely homotopy, homology and the theory of currents. Using these methods, a more direct, but also more sophisticated, approach to the equivalence of the geometric and algebraic classification is made. Background material is introduced gradually to familiarise readers with ideas from areas such as Lie groups, differential topology and probability, in particular, random walks on groups. Numerous open problems inspire students to explore further |
| Beschreibung: | The classification and the first main theorem -- NC-groups -- The B-NB classification -- NB-Groups -- Other classes of locally compact groups -- The geometric theory. An introduction -- The geometric NC-theorem -- Algebra and geometries on C-groups -- The end game in the C-theorem -- The metric classification -- The homotopy and homology classification of connected Lie groups -- The polynomial homology for simply connected soluble groups -- Cohomology on Lie groups Includes bibliographical references and index |
| Beschreibung: | 1 Online-Ressource (xxvii, 596 Seiten) |
| ISBN: | 9781139567718 |
| DOI: | 10.1017/9781139567718 |
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| 500 | |a The classification and the first main theorem -- NC-groups -- The B-NB classification -- NB-Groups -- Other classes of locally compact groups -- The geometric theory. An introduction -- The geometric NC-theorem -- Algebra and geometries on C-groups -- The end game in the C-theorem -- The metric classification -- The homotopy and homology classification of connected Lie groups -- The polynomial homology for simply connected soluble groups -- Cohomology on Lie groups | ||
| 500 | |a Includes bibliographical references and index | ||
| 520 | |a This book provides a complete and reasonably self-contained account of a new classification of connected Lie groups into two classes. The first part describes the use of tools from potential theory to establish the classification and to show that the analytic and algebraic approaches to the classification are equivalent. Part II covers geometric theory of the same classification and a proof that it is equivalent to the algebraic approach. Part III is a new approach to the geometric classification that requires more advanced geometric technology, namely homotopy, homology and the theory of currents. Using these methods, a more direct, but also more sophisticated, approach to the equivalence of the geometric and algebraic classification is made. Background material is introduced gradually to familiarise readers with ideas from areas such as Lie groups, differential topology and probability, in particular, random walks on groups. Numerous open problems inspire students to explore further | ||
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Datensatz im Suchindex
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| author | Varopoulos, N. Th. 1940- |
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| dewey-full | 512/.482 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1017/9781139567718 |
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| id | DE-604.BV046975395 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T15:48:26Z |
| indexdate | 2024-07-10T08:59:05Z |
| institution | BVB |
| isbn | 9781139567718 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032383532 |
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| physical | 1 Online-Ressource (xxvii, 596 Seiten) |
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| publisher | Cambridge University Press |
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| series | New mathematical monographs |
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| spelling | Varopoulos, N. Th. 1940- Verfasser (DE-588)141712228 aut Potential theory and geometry on Lie groups N. Th. Varopoulos Cambridge, United Kingdom ; New York, NY, USA ; Port Melbourne, VIC, Australia ; New Delhi, India ; Singapore Cambridge University Press 2020 1 Online-Ressource (xxvii, 596 Seiten) txt rdacontent c rdamedia cr rdacarrier New mathematical monographs 38 The classification and the first main theorem -- NC-groups -- The B-NB classification -- NB-Groups -- Other classes of locally compact groups -- The geometric theory. An introduction -- The geometric NC-theorem -- Algebra and geometries on C-groups -- The end game in the C-theorem -- The metric classification -- The homotopy and homology classification of connected Lie groups -- The polynomial homology for simply connected soluble groups -- Cohomology on Lie groups Includes bibliographical references and index This book provides a complete and reasonably self-contained account of a new classification of connected Lie groups into two classes. The first part describes the use of tools from potential theory to establish the classification and to show that the analytic and algebraic approaches to the classification are equivalent. Part II covers geometric theory of the same classification and a proof that it is equivalent to the algebraic approach. Part III is a new approach to the geometric classification that requires more advanced geometric technology, namely homotopy, homology and the theory of currents. Using these methods, a more direct, but also more sophisticated, approach to the equivalence of the geometric and algebraic classification is made. Background material is introduced gradually to familiarise readers with ideas from areas such as Lie groups, differential topology and probability, in particular, random walks on groups. Numerous open problems inspire students to explore further Lie groups Geometry Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 s Geometrie (DE-588)4020236-7 s Potenzialtheorie (DE-588)4046939-6 s DE-604 Erscheint auch als Druck-Ausgabe, Hardcover 978-1-107-03649-9 New mathematical monographs 38 (DE-604)BV045935264 38 https://doi.org/10.1017/9781139567718 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Varopoulos, N. Th. 1940- Potential theory and geometry on Lie groups New mathematical monographs Lie groups Geometry Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd Lie-Gruppe (DE-588)4035695-4 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4046939-6 (DE-588)4035695-4 (DE-588)4020236-7 |
| title | Potential theory and geometry on Lie groups |
| title_auth | Potential theory and geometry on Lie groups |
| title_exact_search | Potential theory and geometry on Lie groups |
| title_exact_search_txtP | Potential theory and geometry on Lie groups |
| title_full | Potential theory and geometry on Lie groups N. Th. Varopoulos |
| title_fullStr | Potential theory and geometry on Lie groups N. Th. Varopoulos |
| title_full_unstemmed | Potential theory and geometry on Lie groups N. Th. Varopoulos |
| title_short | Potential theory and geometry on Lie groups |
| title_sort | potential theory and geometry on lie groups |
| topic | Lie groups Geometry Potential theory (Mathematics) Potenzialtheorie (DE-588)4046939-6 gnd Lie-Gruppe (DE-588)4035695-4 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Lie groups Geometry Potential theory (Mathematics) Potenzialtheorie Lie-Gruppe Geometrie |
| url | https://doi.org/10.1017/9781139567718 |
| volume_link | (DE-604)BV045935264 |
| work_keys_str_mv | AT varopoulosnth potentialtheoryandgeometryonliegroups |