A generalization of the original Diffie-Hellman key exchange in (Z/pZ) found a new depth when Miller [27] and Koblitz [16] suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast generalization where abelian semigroups act on finite sets. We define a Diffie-Hellman key exchange in this setting and we illustrate how to build in...

The cone of lower semicontinuous traces is studied with a view to its use as an invariant. Its properties include compactness, Hausdorffness, and continuity with respect to inductive limits. A suitable notion of dual cone is given. The cone of lower semicontinuous 2-quasitraces on a (non-exact) C*-algebra is considered as well. These results are applied to the study of the Cuntz semigroup. It i...

In this paper an algorithm is presented that can be used to calculate the automorphism group of a finite transformation semigroup. The general algorithm employs a special method to compute the automorphism group of a finite simple semigroup. As an application of the algorithm, all the automorphism groups of semigroup of order at most 7 and of the multiplicative semigroups of some group rings ar...

This paper is concerned with emptyness of the essential spectrum, or equivalently compactness of the semigroup, for perturbations of selfadjoint operators that are bounded below (on an L2-space). For perturbations by a (nonnegative) potential we obtain a simple criterion for compactness of the semigroup in terms of relative compactness of the operators of multiplication with characteristic func...

The basic properties of the cones of lower semicontinuous traces and 2-quasitraces are studied. These properties include: compactness and Hausdorffness of the given cone, continuity of the corresponding functor, and a suitable notion of dual space. These results are applied to the study of the Cuntz semigroup of some classes of C*-algebras. It is shown that if a C*-algebra absorbs the Jiang-Su ...

We describe our construction of a continuous tensor product system in the sense of Arveson for a general W ∗-continuous completely positive semigroup of B(H) (H separable). This product system is canonically isomorphic to the product system of the minimal dilation E0-semigroup. We use this construction to show that contrary to previous speculation the minimal dilations of all quantized convolut...

In this paper we study the operator inequality φ(X) ≤ X and the operator equation φ(X) = X, where φ is a w∗-continuous positive (resp. completely positive) linear map on B(H). We show that their solutions are in one-to-one correspondence with a class of Poisson transforms on Cuntz-Toeplitz C∗-algebras, if φ is completely positive. Canonical decompositions, ergodic type theorems, and lifting the...