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Cover: 9783540547457 | Kac Algebras and Duality of Locally Compact Groups | Enock (u. a.) | x
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Kac Algebras and Duality of Locally Compact Groups
Buch von Michel Enock (u. a.)
Sprache: Englisch

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Beschreibung
This book deals with the theory of Kac algebras and their dual­ ity, elaborated independently by M. Enock and J . -M. Schwartz, and by G. !. Kac and L. !. Vajnermann in the seventies. The sub­ ject 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 character­ ization 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. !. 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.
This book deals with the theory of Kac algebras and their dual­ ity, elaborated independently by M. Enock and J . -M. Schwartz, and by G. !. Kac and L. !. Vajnermann in the seventies. The sub­ ject 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 character­ ization 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. !. 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.
Inhaltsverzeichnis
1. Co-Involutive Hopf-Von Neumann Algebras.- 2. Kac Algebras.- 3. Representations of a Kac Algebra; Dual Kac Algebra.- 4. Duality Theorems for Kac Algebras and Locally Compact Groups.- 5. The Category of Kac Algebras.- 6. Special Cases: Unimodular, Compact, Discrete and Finite-Dimensional Kac Algebras.- Postface.
Details
Erscheinungsjahr: 1992
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: x
257 S.
1 s/w Illustr.
ISBN-13: 9783540547457
ISBN-10: 3540547452
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Enock, Michel
Schwartz, Jean-Marie
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 241 x 160 x 20 mm
Von/Mit: Michel Enock (u. a.)
Erscheinungsdatum: 14.12.1992
Gewicht: 0,582 kg
Artikel-ID: 102136317
Inhaltsverzeichnis
1. Co-Involutive Hopf-Von Neumann Algebras.- 2. Kac Algebras.- 3. Representations of a Kac Algebra; Dual Kac Algebra.- 4. Duality Theorems for Kac Algebras and Locally Compact Groups.- 5. The Category of Kac Algebras.- 6. Special Cases: Unimodular, Compact, Discrete and Finite-Dimensional Kac Algebras.- Postface.
Details
Erscheinungsjahr: 1992
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: x
257 S.
1 s/w Illustr.
ISBN-13: 9783540547457
ISBN-10: 3540547452
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Enock, Michel
Schwartz, Jean-Marie
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 241 x 160 x 20 mm
Von/Mit: Michel Enock (u. a.)
Erscheinungsdatum: 14.12.1992
Gewicht: 0,582 kg
Artikel-ID: 102136317
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