The canonical trace on the reduced C∗-algebra of a discrete group gives rise to a homomorphism from the K-theory of this C∗-algebra to the real numbers. This paper studies the range of this homomorphism. For torsion free groups, the Baum-Connes conjecture together with Atiyah’s L-index theorem implies that the range consists of the integers. We give a direct and elementary proof that if G acts ...

The canonical trace on the reduced C∗-algebra of a discrete group gives rise to a homomorphism from the K-theory of this C∗-algebra to the real numbers. This paper studies the range of this homomorphism. For torsion free groups, the Baum-Connes conjecture together with Atiyah’s L-index theorem implies that the range consists of the integers. We give a direct and elementary proof that if G acts ...

Some completely positive maps on reduced amalgamated free products of C∗–algebras are constructed, showing that every reduced amalgamated free product of exact C∗–algebras is exact. Consequently, every amalgamated free product of exact discrete groups is exact.

Amalgamated graph transformation allows to define schemes of rules coinciding in common core activities and differing over additional parallel independent activities. Consequently, a rule scheme is specified by a kernel rule and a set of extending multi-rules forming an interaction scheme. Amalgamated transformations have been increasingly used in various modeling contexts. Critical Pair Analys...

The theory of Amalgamated Knowledge' Bases [7] represents a formal logical foundation for heterogeneous databases. In an Amalgamated Knowledge Base, data sources are modeled by generalized annotated logic. Moreover, an Amalgamated Knowledge Base is equipped with a supervisor acting as a mediator for amalgamating knowledge from the local databases. Even if the framework is quite appealing, it do...

Based on cosmogenic 10Be and 26Al analyses in 15 individual detrital quartz pebbles (16–21 mm) and cosmogenic 10Be in amalgamated medium sand (0.25–0.50 mm), all collected from the outlet of the upper Gaub River catchment in Namibia, quartz pebbles yield a substantially lower average denudation rate than those yielded by the amalgamated sand sample. 10Be and 26Al concentrations in the 15 indivi...

Amalgamated free products of von Neumann algebras were first used by S. Popa ([26]) to construct an irreducible inclusion of (non-AFD) type II1 factors with an arbitrary (admissible) Jones index. Further investigation in this direction was made by K. Dykema ([10]) and F. Rădulescu ([27, 29]) based on Voiculescu’s powerful machine ([40, 41, 44]), and F. Boca ([4]) discussed the Haagerup approxim...

We prove that the amalgamated product of free groups with cyclic amalgamations satisfying certain conditions are virtually free-by-cyclic. In case the cyclic amalgamated subgroups lie outside the derived group such groups are free-by-cyclic. Similarly a one-relator HNN-extension in which the conjugated elements either coincide or are independent modulo the derived group is shown to be free-by-c...

In this paper we collect a few results about exchangeability systems in which crossing cumulants vanish, which we call noncrossing exchangeability systems. De Finetti’s theorem states that any exchangeable sequence of random variables is conditionally i.i.d. with respect to some σ-algebra. In this paper we prove a “free” noncommutative analog of this theorem, namely we show that any noncrossing...