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We give a decomposition of the equivariant Kasparov category for discrete quantum group with torsions. As an outcome, we show that the crossed product by a discrete quantum group in a certain class preserves the UCT. We then show that…

Let $\M=P\times{M}$ be a variable Mautner group. We describe the $C^*$-algebra $C^*(\M)$ of $\M$ in terms of an algebra of operator fields defined over $P\times{\C^2} $.

A discrete countable group G is matricially stable if the finite dimensional approximate unitary representations of G are perturbable to genuine representations in the point-norm topology. For large classes of groups G, we show that…

We present some results concerning the relative modular operator in semifinite von Neumann algebras. These results allow one to prove some basic formula for trace, to obtain equivalence between Araki's relative entropy and Umegaki's…

We prove that a Bieberbach group with trivial center is not connective and use this property to show that a Bieberbach group is connective if and only if it is poly-Z.

We establish a platform to transfer $L_p$-completely bounded maps on tensor products of von Neumann algebras to $L_p$-completely bounded maps on the corresponding amalgamated free products. As a consequence, we obtain a H\"ormander-Mikhlin…

We prove that it is consistent with ZFC that every unital endomorphism of the Calkin algebra $\mathcal{Q}(H)$ is unitarily equivalent to an endomorphism of $\mathcal{Q}(H)$ which is liftable to a unital endomorphism of $\mathcal{B}(H)$. We…

We study the phase transition of KMS states for the C*-algebras of $ax+b$-semigroups of algebraic integers in which the multiplicative part is restricted to a congruence monoid, as in recent work of Bruce generalizing earlier work of Cuntz,…

We compute the KMS (equilibrium) states for the canonical time evolution on C*-algebras from actions of congruence monoids on rings of algebraic integers. We show that for each $\beta\in[1,2]$, there is a unique KMS$_\beta$ state, and we…

A locally compact groupoid is said to have the weak containment property if its full $C^*$-algebra coincides with its reduced one. This property is strictly weaker than amenability and is known to be equivalent to amenability for…

Let $M\subset B(\mathcal H)$ be a von Neumann algebra acting on the Hilbert space $\mathcal H$. We prove that $M$ is finite if and only if, for every $x\in M$ and for all vectors $\xi,\eta\in\mathcal H$, the coefficient function $u\mapsto…

The Podles quantum sphere S^2_q admits a natural commutative C*-subalgebra I_q with spectrum {0} \cup {q^{2k}: k = 0,1,2,...}, which may therefore be considered as a quantised version of a classical interval. We study here the compact…

Given an action of a compact group on a complex vector bundle, there is an induced action of the group on the associated Cuntz-Pimsner algebra. We determine conditions under which this action has finite Rokhlin dimension.

Alain Connes and Nigel Higson pointed out in the 1990s that the Connes-Kasparov "conjecture"' for the K-theory of reduced groupe $C^\ast$-algebras seemed, in the case of reductive Lie groups, to be a cohomological echo of a conjecture of…

In this paper we generalize the results shown by Das and Peterson. Let $M$ be a ${\rm II}_1$-factor acting on $L^2(M)$. We consider certain unital normal completely positive maps on $B(L^2(M))$ which are identity on $M$. We investigate…

Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…

We study the $C^*$-algebra $\mathcal{T}/\mathcal{K}$ where $\mathcal{T}$ is the $C^*$-algebra generated by $d$ weighted shifts on the Fock space of $\mathbb{C}^d$, $\mathcal{F}(\mathbb{C}^d)$, ( where the weights are given by a sequence…

In recent joint work of the authors with Laca, we precisely formulated the notion of partition function in the context of C*-dynamical systems. Here, we compute the partition functions of C*-dynamical systems arising from Toeplitz algebras…

We revisit and generalize the application of a method introduced by Latr\'emoli\`ere and Packer for constructing finitely generated projective modules over the noncommutative solenoid C*-algebras. By realizing them as direct limits of…

The Sierpinski gasket admits a locally isometric ramified self-covering. A semifinite spectral triple is constructed on the resulting solenoidal space, and its main geometrical features are discussed.