By improving the previous construction in [18] we observe that any reduced HNN extension is a corner of a certain reduced amalgamated free product in both the von Neumann algebra and the C∗-algebra settings. Then, the same fact is shown for universal HNN extensions of C∗-algebras. We apply the observation to the questions of factoriality and type classification of HNN extensions of von Neumann ...

By weakening the counit and antipode axioms of a C∗-Hopf algebra and allowing for the coassociative coproduct to be non-unital we obtain a quantum group, that we call a weak C∗Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. This amounts to generalizing the Baaj-Skandalis multiplicative unitaries to multipicative partial isometries. E...

A countable discrete group G is called W?-superrigid (resp. C?-superrigid) if it completely recognizable from its von Neumann algebra L(G) reduced C?-algebra Cr?(G)). Developing new technical aspects in Popa's deformation/rigidity theory we introduce several classes of groups which appear as direct products, semidirect products with non-amenable core and iterations amalgamated free HNN-extensio...

For each 1 < s < ∞, a Popa algebra As is constructed that embeds as a weakly dense C∗–subalgebra of the interpolated free group factor L(Fs). Certain approximation properties for As are shown. It follows that L(Fs) has the weak expectation property of Lance with respect to As. In the course of the demonstration, it is proved that under certain conditions, full amalgamated free products of matri...

When combining languages for symbolic constraints, one is typically faced with the problem of how to treat \mixed" constraints. The two main problems are (1) how to deene a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint solving methods for pure constraints into one for mixed constraints. The paper introduces the notion of a \free...

The main purpose of this article is to study pro-p groups with quadratic Fp-cohomology algebra, i.e. H•-quadratic groups. Prime examples such are the maximal Galois fields containing a primitive root unity order p. We show that amalgamated free product and HNN-extension H•-quadratic, under certain necessary conditions. Moreover, we introduce investigate new family yields many groups: p-RAAGs. T...

We give a construction of a nuclear C∗-algebra associated with an amalgamated free product of groups, generalizing Spielberg’s construction of a certain Cuntz-Krieger algebra associated with a finitely generated free product of cyclic groups. Our nuclear C∗-algebras can be identified with certain Cuntz-Krieger-Pimsner algebras. We will also show that our algebras can be obtained by the crossed ...

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 addresses the range of this homomorphism. For torsion free groups, the Baum-Connes conjecture and Atiyah’s L-index theorem implies that the range consists of the integers. If the group is not torsion free, Baum and Connes conjecture ...