Distributive nearlattices with a necessity modal operator

The aim of this paper is to study the class of distributive nearlattices with a necessity modal operator. We develop a full duality to the category of distributive nearlattices whose morphisms are applications that preserving the infimum when exists and, as special case, we obtain a representation and duality for distributive nearlattices with a necessity modal operator. We study certain particular subclasses and give some applications.

DUALITY OF HOPF C*-ALGEBRAS

In this paper, we study the duality theory of Hopf C*-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*-algebra. This study of reduced duality and Fourier algebra is found to be useful in the study of other aspects of Hopf C*-algebras (see e.g. [12–14]).

Full duality for coactions of discrete groups

Using the strong relation between coactions of a discrete group $G$ on $C^*$-algebras and Fell bundles over $G$ we prove a new version of Mansfield's imprimitivity theorem for coactions of discrete groups. Our imprimitivity theorem works for the universally defined full crossed products and arbitrary subgroups of $G$ as opposed to the usual theory of [16], [11] which uses the spatially defined reduced crossed products and normal subgroups of $G$. Moreover, our theorem factors through the usual one by passing to appropriate quotients. As applications we show that a Fell bundle over a discrete group is amenable in the sense of Exel [7] if and only if the double dual action is amenable in the sense that the maximal and reduced crossed products coincide. We also give a new characterization of induced coactions in terms of their dual actions.

SPACETIME DUALITY AND $\frac{{{\rm{SU}}\left( {n,\,1} \right)}}{{{\rm{SU}}\left( n \right) \otimes {\rm{U}}\left( 1 \right)}}$ COSETS OF ORBIFOLD COMPACTIFICATION

The duality symmetry group of the cosets [Formula: see text] which describe the moduli space of a two-dimensional subspace of an orbifold model with (n – 1) complex Wilson lines moduli, is discussed. The full duality group and its explicit action on the moduli fields are derived.