Related papers: Nica-Toeplitz algebras associated with right tenso…

We prove uniqueness of representations of Nica-Toeplitz algebras associated to product systems of $C^*$-correspondences over right LCM semigroups by applying our previous abstract uniqueness results developed for $C^*$-precategories. Our…

We introduce and analyse the structure of C*-algebras arising from ideals in right tensor C*-precategories, which naturally generalize both relative Cuntz-Pimsner and Doplicher-Roberts algebras. We establish an explicit intrinsic…

To a graph $\Gamma$ one can associate a C^*-algebra $C^*(\Gamma)$ generated by isometries. Such $C^*$-algebras were studied recently by Crisp and Laca. They are a special case of the Toeplitz C^*-algebras $\mathcal{T}(G, P)$ associated to…

Fowler introduced the notion of a product system: a collection of Hilbert bimodules $\mathbf{X}=\left\{\mathbf{X}_p:p\in P\right\}$ indexed by a semigroup $P$, endowed with a multiplication implementing isomorphisms $\mathbf{X}_p\otimes_A…

We introduce algebraic dynamical systems, which consist of an action of a right LCM semigroup by injective endomorphisms of a group. To each algebraic dynamical system we associate a C*-algebra and describe it as a semigroup C*-algebra. As…

We construct reduced and full semigroup C*-algebras for left cancellative semigroups. Our new construction covers particular cases already considered by A. Nica and also Toeplitz algebras attached to rings of integers in number fields due…

Let (G,P) be a quasi-lattice ordered group and let X be a compactly aligned product system over P of Hilbert bimodules. Under mild hypotheses we associate to X a C*-algebra which we call the Cuntz-Nica-Pimsner algebra of X. Our construction…

Let X be a product system over a quasi-lattice ordered group. Under mild hypotheses, we associate to X a C*-algebra which is co-universal for injective Nica covariant Toeplitz representations of X which preserve the gauge coaction. Under…

The graph product of a family of groups lies somewhere between their direct and free products, with the graph determining which pairs of groups commute and which do not. We show that the graph product of quasi-lattice ordered groups is…

We associate with the ring $R$ of algebraic integers in a number field a C*-algebra $\cT[R]$. It is an extension of the ring C*-algebra $\cA[R]$ studied previously by the first named author in collaboration with X.Li. In contrast to…

For special universal $C^*$-algebras associated to $k$-semigraphs we present the universal representations of these algebras, prove a Cuntz--Krieger uniqueness theorem, and compute the $K$-theory. These $C^*$-algebras seem to be the most…

Consider the pair $(G,P)$ consisting of an abelian lattice-ordered discrete group $G$ and its positive cone $P$. Let $\alpha$ be an action of $P$ by extendible endomorphisms of a $C^*$-algebra $A$. We show that the Nica-Toeplitz algebra…

We show that the group ${\mathbb Q \rtimes \mathbb Q^*_+}$ of orientation-preserving affine transformations of the rational numbers is quasi-lattice ordered by its subsemigroup ${\mathbb N \rtimes \mathbb N^\times}$. The associated Toeplitz…

We prove a version of uniqueness theorem for Cuntz-Pimsner algebras of discrete product systems over semigroups of Ore type. To this end, we introduce Doplicher-Roberts picture of Cuntz-Pimsner algebras, and the semigroup dual to a product…

We investigate KMS states of Fowler's Nica-Toeplitz algebra $\mathcal{NT}(X)$ associated to a compactly aligned product system $X$ over a semigroup $P$ of Hilbert bimodules. This analysis relies on restrictions of these states to the core…

We introduce the notion of a self-similar action of a groupoid $G$ on a finite higher-rank graph. To these actions we associate a compactly aligned product system of Hilbert bimodules, and thereby obtain corresponding universal…

We consider the semigroup crossed product of the additive natural numbers by the multiplicative natural numbers. We study its Toeplitz C*-algebra generated by the right-regular representation, which we call the right Toeplitz algebra. We…

Consider a product system over the positive cone of a quasi-lattice ordered group. We construct a Fell bundle over an associated groupoid so that the cross-sectional algebra of the bundle is isomorphic to the Nica-Toeplitz algebra of the…

Let $X$ be a product system over a quasi-lattice ordered groupoid $(G,P)$. Under mild hypotheses, we associate to $X$ a $C^*$-algebra which is couniversal for injective Nica covariant Toeplitz representations of $X$ which preserve the gauge…

We introduce the notion of K-theoretic duality for extensions of separable unital nuclear $C^*$-algebras by using K-homology long exact sequence and cyclic six term exact sequence for K-theory groups of extensions. We then prove that the…