Duality of Hopf $C^{\ast }$-algebras

Abstract

In this paper, we study the duality theory of Hopf $C^{\ast }$-algebras in a general ``Hilbert-space-free'' framework. Our particular interests are the ``full duality'' and the ``reduced duality''. In order to study the reduced duality, we define the interesting notion of Fourier algebra of a general Hopf $C^{\ast }$-algebra.

It is a shortened version of a paper with the same title that was in circulation since 1998. To be published in the International Journal of Mathematics