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Kac Algebras and Duality of Locally Compact Groups (Paperback, Softcover reprint of hardcover 1st ed. 1992)
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Kac Algebras and Duality of Locally Compact Groups (Paperback, Softcover reprint of hardcover 1st ed. 1992)
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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.
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