The Structure of Pro-Lie Groups
Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonné quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them. A *pro-Lie group* is a complete topological group *G* in which every identi...
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| Главные авторы: | , |
|---|---|
| Формат: | Livre numérique |
| Язык: | Anglais |
| Опубликовано: |
Berlin :
European Mathematical Society
2023.
Berlin : |
| Серии: | EMS Tracts in Mathematics
36 |
| Online-ссылка: | Accès sur la plateforme EMS Press Accès sur la plateforme ISTEX Accès Université d'Orléans Accès INSA CVL |
| Примечание: |
European Mathematical Society (Licence nationale) European Mathematical Society (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • The Structure of Pro-Lie Groups, 978-3-98547-048-8 |
| LEADER | 03947nam a22003737a 4500 | ||
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| 084 | |a 22-02. 2020 | ||
| 084 | |a 22A05. 2020 | ||
| 084 | |a 22D05. 2020 | ||
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| 084 | |a 22-02. 2020 | ||
| 100 | 1 | |a Hofmann, Karl Heinrich, |d 1932- | |
| 245 | 1 | 0 | |a The Structure of Pro-Lie Groups |c Karl H. Hofmann, Sidney A. Morris. |
| 260 | |a Berlin : |b European Mathematical Society. | ||
| 260 | |a Berlin : |b European Mathematical Society, |c 2023. | ||
| 490 | 0 | |a EMS Tracts in Mathematics |x 2943-5005 |v 36 | |
| 500 | |a European Mathematical Society (Licence nationale) | ||
| 500 | |a European Mathematical Society (Licence nationale) | ||
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/wp-content/uploads/2022/07/EMS_ebooks_LN_CollEx_contrat.pdf | ||
| 520 | |a Lie groups were introduced in 1870 by the Norwegian mathematician Sophus Lie. A century later Jean Dieudonné quipped that Lie groups had moved to the center of mathematics and that one cannot undertake anything without them. A *pro-Lie group* is a complete topological group *G* in which every identity neighborhood *U* of *G* contains a normal subgroup *N* such that the quotient *G/N* is a Lie group. Every locally compact connected topological group and every compact group is a pro-Lie group. While the class of locally compact groups is not closed under the formation of arbitrary products, the class of pro-Lie groups is. For half a century, locally compact pro-Lie groups have drifted through the literature, yet this is the first book which systematically treats the Lie theory and the structure theory of pro-Lie groups irrespective of local compactness. So it fits very well into that current trend which addresses infinite dimensional Lie groups. The results of this text are based on a theory of pro-Lie algebras which parallels the structure theory of finite dimensional real Lie algebras to an astonishing degree even though it has to overcome technical obstacles. A topological group is said to be almost connected if the quotient group of its connected components is compact. This book exposes a Lie theory of almost connected pro-Lie groups (and hence of almost connected locally compact groups) and illuminates the variety of ways in which their structure theory reduces to that of compact groups on the one hand and of finite dimensional Lie groups on the other. It is therefore a continuation of the authors' monograph on the structure of compact groups (1998, 2006, 2014, 2020, 2023) and is an invaluable tool for researchers in topological groups, Lie theory, harmonic analysis and representation theory. It is written to be accessible to advanced graduate students wishing to study this fascinating and important area of research, which has so many fruitful interactions with other fields of mathematics. | ||
| 700 | 1 | |a Morris, Sidney A., |d 1947- |4 aut | |
| 776 | 0 | |t The Structure of Pro-Lie Groups |z 978-3-98547-048-8 | |
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