00 3 Sup - lattice 2 - forms and quantales ∗

00 2 Sup - lattice 2 - forms and quantales ∗

A 2-form between two sup-lattices L and R is defined to be a suplattice bimorphism L×R → 2. Such 2-forms are equivalent to Galois connections, and we study them and their relation to quantales, involutive quantales and quantale modules. As examples we describe applications to C*-algebras.

ar X iv : m at h . R A / 0 21 13 20 v 2 9 D ec 2 00 3 Sup - lattice 2 - forms and quantales ∗

A 2-form between two sup-lattices L and R is defined to be a suplattice bimorphism L×R → 2. Such 2-forms are equivalent to Galois connections, and we study them and their relation to quantales, involutive quantales and quantale modules. As examples we describe applications to C*-algebras.

Sup-Lattice 2-Forms and Quantales

On Simple and Semisimple Quantales

In a recent paper [7], J. W. Pelletier and J. Rosický published a characterization of *-simple *-quantales. Their results were adapted for the case of simple quantales by J. Paseka in [5]. In this paper we present similar characterizations which do not use a notion of discrete quantale. We also show a completely new characterization based on separating and cyclic sets. Further we explain a link...

Girard Couples of Quantales

We introduce the concept of a Girard couple, which consists of two (not necessarily unital) quantales linked by a strong form of duality. The two basic examples of Girard couples arise in the study of endomorphism quantales and of the spectra of operator algebras. We construct, for an arbitrary sup-lattice S, a Girard quantale whose right-sided part is isomorphic to S.