Kac Algebras and Duality of Locally Compact Groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1992
|
| Subjects: | |
| Links: | https://doi.org/10.1007/978-3-662-02813-1 |
| Item Description: | This book deals with the theory of Kac algebras and their duality, elaborated independently by M. Enock and J . -M. Schwartz, and by G. I. Kac and L. I. Vajnermann in the seventies. The subject has now reached a state of maturity which fully justifies the publication of this book. Also, in recent times, the topic of "quantum groups" has become very fashionable and attracted the attention of more and more mathematicians and theoret ical physicists. One is still missing a good characterization of quantum groups among Hopf algebras, similar to the characterization of Lie groups among locally compact groups. It is thus extremely valuable to develop the general theory, as this book does, with emphasis on the analytical aspects of the subject instead of the purely algebraic ones. The original motivation of M. Enock and J. -M. Schwartz can be formulated as follows: while in the Pontrjagin duality theory of locally compact abelian groups a perfect symmetry exists between a group and its dual, this is no longer true in the various duality theorems of T. Tannaka, M. G. Krein, W. F. Stinespring . . . dealing with non abelian locally compact groups. The aim is then, in the line proposed by G. I. Kac in 1961 and M. Takesaki in 1972, to find a good category of Hopf algebras, containing the category of locally compact groups and fulfilling a perfect duality |
| Physical Description: | 1 Online-Ressource (X, 257 p) |
| ISBN: | 9783662028131 9783642081286 |
| DOI: | 10.1007/978-3-662-02813-1 |
Staff View
MARC
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| 500 | |a This book deals with the theory of Kac algebras and their duality, elaborated independently by M. Enock and J . -M. Schwartz, and by G. I. Kac and L. I. Vajnermann in the seventies. The subject has now reached a state of maturity which fully justifies the publication of this book. Also, in recent times, the topic of "quantum groups" has become very fashionable and attracted the attention of more and more mathematicians and theoret ical physicists. One is still missing a good characterization of quantum groups among Hopf algebras, similar to the characterization of Lie groups among locally compact groups. It is thus extremely valuable to develop the general theory, as this book does, with emphasis on the analytical aspects of the subject instead of the purely algebraic ones. The original motivation of M. Enock and J. -M. Schwartz can be formulated as follows: while in the Pontrjagin duality theory of locally compact abelian groups a perfect symmetry exists between a group and its dual, this is no longer true in the various duality theorems of T. Tannaka, M. G. Krein, W. F. Stinespring . . . dealing with non abelian locally compact groups. The aim is then, in the line proposed by G. I. Kac in 1961 and M. Takesaki in 1972, to find a good category of Hopf algebras, containing the category of locally compact groups and fulfilling a perfect duality | ||
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Record in the Search Index
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| id | DE-604.BV042423217 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:48Z |
| institution | BVB |
| isbn | 9783662028131 9783642081286 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858634 |
| oclc_num | 1184505608 |
| open_access_boolean | |
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| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (X, 257 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| spellingShingle | Enock, Michel Kac Algebras and Duality of Locally Compact Groups Mathematics Algebra Topological Groups Harmonic analysis Topological Groups, Lie Groups Associative Rings and Algebras Non-associative Rings and Algebras Abstract Harmonic Analysis Mathematik Dualität (DE-588)4013161-0 gnd Lokal kompakte Gruppe (DE-588)4168094-7 gnd Kac-Algebra (DE-588)4304563-7 gnd |
| subject_GND | (DE-588)4013161-0 (DE-588)4168094-7 (DE-588)4304563-7 |
| title | Kac Algebras and Duality of Locally Compact Groups |
| title_auth | Kac Algebras and Duality of Locally Compact Groups |
| title_exact_search | Kac Algebras and Duality of Locally Compact Groups |
| title_full | Kac Algebras and Duality of Locally Compact Groups by Michel Enock, Jean-Marie Schwartz |
| title_fullStr | Kac Algebras and Duality of Locally Compact Groups by Michel Enock, Jean-Marie Schwartz |
| title_full_unstemmed | Kac Algebras and Duality of Locally Compact Groups by Michel Enock, Jean-Marie Schwartz |
| title_short | Kac Algebras and Duality of Locally Compact Groups |
| title_sort | kac algebras and duality of locally compact groups |
| topic | Mathematics Algebra Topological Groups Harmonic analysis Topological Groups, Lie Groups Associative Rings and Algebras Non-associative Rings and Algebras Abstract Harmonic Analysis Mathematik Dualität (DE-588)4013161-0 gnd Lokal kompakte Gruppe (DE-588)4168094-7 gnd Kac-Algebra (DE-588)4304563-7 gnd |
| topic_facet | Mathematics Algebra Topological Groups Harmonic analysis Topological Groups, Lie Groups Associative Rings and Algebras Non-associative Rings and Algebras Abstract Harmonic Analysis Mathematik Dualität Lokal kompakte Gruppe Kac-Algebra |
| url | https://doi.org/10.1007/978-3-662-02813-1 |
| work_keys_str_mv | AT enockmichel kacalgebrasanddualityoflocallycompactgroups AT schwartzjeanmarie kacalgebrasanddualityoflocallycompactgroups |