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2 produkter
1 062 kr
Skickas inom 10-15 vardagar
The theory of Kac lagebras and their duality, elaboratedindependently in the seventies by Kac and Vainermann and bythe authors of this book, has nowreached a state ofmaturity which justifies the publication of a comprehensiveand authoritative account in bookform. Further, the topic of"quantum groups" has recently become very fashionable andattracted the attention of more and more mathematicians andtheoretical physicists. However a good characterization ofquantum groups among Hopf algebras in analogy to thecharacterization of Lie groups among locally compact groupsis still missing. It is thus very valuable to develop thegeneraltheory as does this book, with emphasis on theanalytical aspects of the subject instead of the purelyalgebraic ones. While in the Pontrjagin duality theory of locally compactabelian groups a perfect symmetry exists between a group andits dual, this is no longer true in the various dualitytheorems of Tannaka, Krein, Stinespring and others dealingwith non-abelian locally compact groups.Kac (1961) andTakesaki (1972) formulated the objective of finding a goodcategory of Hopf algebras, containing the category oflocally compact groups and fulfilling a perfect duality. The category of Kac algebras developed in this book fullyanswers the original duality problem, while not yetsufficiently non-unimodular to include quantum groups. This self-contained account of thetheory will be ofinterest to all researchers working in quantum groups,particularly those interested in the approach by Lie groupsand Lie algebras or by non-commutative geometry, and moregenerally also to those working in C* algebras ortheoretical physics.
1 062 kr
Skickas inom 10-15 vardagar
The theory of Kac lagebras and their duality, elaborated independently in the seventies by Kac and Vainermann and by the authors of this book, has nowreached a state of maturity which justifies the publication of a comprehensive and authoritative account in bookform. Further, the topic of "quantum groups" has recently become very fashionable and attracted the attention of more and more mathematicians and theoretical physicists. However a good characterization of quantum groups among Hopf algebras in analogy to the characterization of Lie groups among locally compact groups is still missing. It is thus very valuable to develop the generaltheory as does this book, with emphasis on the analytical aspects of the subject instead of the purely algebraic ones. 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 Tannaka, Krein, Stinespring and others dealing with non-abelian locally compact groups.Kac (1961) and Takesaki (1972) formulated the objective of finding a good category of Hopf algebras, containing the category of locally compact groups and fulfilling a perfect duality. The category of Kac algebras developed in this book fully answers the original duality problem, while not yet sufficiently non-unimodular to include quantum groups. This self-contained account of thetheory will be of interest to all researchers working in quantum groups, particularly those interested in the approach by Lie groups and Lie algebras or by non-commutative geometry, and more generally also to those working in C* algebras or theoretical physics.