相关论文: Approximating the group algebra of the lamplighter…

We compute the C*-algebra generated by a group of composition operators acting on certain reproducing kernel Hilbert spaces over the disk, where the symbols belong to a non-elementary Fuchsian group. We show that such a C*-algebra contains…

The analytic von Neumann regular closure $R(\Gamma)$ of a complex group algebra $\C\Gamma$ was introduced by Linnell and Schick. This ring is the smallest $*$-regular subring in the algebra of affiliated operators $U(\Gamma)$ containing…

The notion of qausi-product actions of a compact group on a C$^*$-algebra was introduced by Bratteli et al. in their attempt to seek an equivariant analogue of Glimm's characterization of non-type I C$^*$-algebras. We show that a faithful…

Given a group $G$, we write $g^G$ for the conjugacy class of $G$ containing the element $g$. A theorem of B. H. Neumann states that if $G$ is a group in which all conjugacy classes are finite with bounded size, then the commutator subgroup…

We extend the construction of generalized fixed point algebras to the setting of locally compact quantum groups - in the sense of Kustermans and Vaes - following the treatment of Marc Rieffel, Ruy Exel and Ralf Meyer in the group case. We…

We introduce a new class of C^*-algebras, which is a generalization of both graph algebras and homeomorphism C^*-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the…

For a locally compact group G and a compact subgroup K, the corresponding Hecke algebra consists of all continuous compactly supported complex functions on G that are K-bi-invariant. There are many examples of totally disconnected locally…

If A is a C*-algebra, G a locally compact group, K{\subset}G a compact subgroup and {\alpha}:G{\to}Aut(A) a continuous homomorphism, let Ax_{{\alpha}}G denote the crossed product. In this paper we prove that Ax_{{\alpha}}G is nuclear…

We initiate a mathematically rigorous study of Klein-Gordon position operators in single-particle relativistic quantum mechanics. Although not self-adjoint, these operators have real spectrum and enjoy a limited form of spectral…

We study the C*-algebra crossed-product of the closed unit disk by the action of one of its conformal automorphisms. After classifying the conformal automorphisms up to topological conjugacy, we investigate, for each class, the irreducible…

We are interested in the McKay quiver $\Gamma(G)$ and skew group rings $A*G$, where $G$ is a finite subgroup of $\mathrm{GL}(V)$, where $V$ is a finite dimensional vector space over a field $K$, and $A$ is a $K-G$-algebra. These skew group…

For every natural number k we prove a decomposition theorem for bounded measurable functions on compact abelian groups into a structured part, a quasi random part and a small error term. In this theorem quasi randomness is measured with the…

A simple Steinberg algebra associated to an ample Hausdorff groupoid $G$ is algebraically purely infinite if and only if the characteristic functions of compact open subsets of the unit space are infinite idempotents. If a simple Steinberg…

Let $G$ be a discrete group acting on a von Neumann algebra $M$ by properly outer $*$-automorphisms. In this paper we study the containment $M \subseteq M\rtimes_\alpha G$ of $M$ inside the crossed product. We characterize the intermediate…

Let $G$ be a locally compact group. Consider the C$^*$-algebra $C_0(G)$ of continuous complex functions on $G$, tending to 0 at infinity. The product in $G$ gives rise to a coproduct $\Delta_G$ on the C$^*$-algebra $C_0(G)$. A locally…

For any finite Coxeter system $(W,S)$ we construct a certain noncommutative algebra, so-called {\it bracket algebra}, together with a familiy of commuting elements, so-called {\it Dunkl elements.} Dunkl elements conjecturally generate an…

Let $F$ be a finite group. We consider the lamplighter group $L=F\wr\mathbb{Z}$ over $F$. We prove that $L$ has a classifying space for proper actions $\underline{E} L$ which is a complex of dimension two. We use this to give an explicit…

von Neumann algebras have been playing an increasingly important role in the context of gauge theories and gravity. The crossed product presents a natural method for implementing constraints through the commutation theorem, rendering it a…

In this paper we study various rigidity aspects of the von Neumann algebra $L(\Gamma)$ where $\Gamma$ is a graph product group \cite{Gr90} whose underlying graph is a certain cycle of cliques and the vertex groups are the wreath-like…

Given a locally compact second countable group $G$ with a 2-cocycle $\omega$, we show that the restriction of the twisted Plancherel weight $\varphi^\omega_G$ to the subalgebra generated by a closed subgroup $H$ in the twisted group von…