Related papers: Kawada-It\^o-Kelley Theorem for Quantum Semigroups

We introduce the Property of Rapid Decay for discrete quantum groups by equivalent characterizations that generalize the classical ones. We then investigate examples, proving in particular the Property of Rapid Decay for unimodular free…

We study the steady-state properties of quantum channels with local Kraus operators. We consider a large family that consists of general ergodic 1-local (non-interacting) terms and general 2-local (interacting) terms. Physically, a repeated…

To any compact $K\subset\hat{\mathbb{C}}$ we associate a map $\lambda_K: \hat{\mathbb{C}}\rightarrow\mathbb{N}\cup\{\infty\}$ -- the lambda function of $K$ -- such that a planar continuum $K$ is locally connected if and only if…

For second countable discrete quantum groups, and more generally second countable locally compact quantum groups with trivial scaling group, we show that property (T) is equivalent to every weakly mixing unitary representation not having…

On a locally compact group we introduce covariant quantization schemes and analogs of phase space representations as well as mixed-state localization operators. These generalize corresponding notions for the affine group and the Heisenberg…

A field $K$ is quasi-classical $d$-local if there exist fields $K=k_d,\dots,k_0$ with $k_{i+1}$ Henselian admissible discretely valued with residue field $k_i$, and $k_0$ quasi-finite. We prove a duality theorem for the Galois cohomology of…

The lattice of subgroups of a group is the subject of numerous results revolving around the central theme of decomposing the group into "chunks" (subquotients) that can then be compared to one another in various ways. Examples of results in…

Quantum embedding theories are promising approaches to investigate strongly-correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We…

Let $c:\mathcal{G}\to\R$ be a cocycle on a locally compact Hausdorff groupoid $\mathcal{G}$ with Haar system. Under some mild conditions (satisfied by all integer valued cocycles on \'{e}tale groupoids), $c$ gives rise to an unbounded odd…

Gazeau-Klauder coherent states in noncommutative quantum mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position…

Subsystems of composite quantum systems are described by reduced density matrices, or quantum marginals. Important physical properties often do not depend on the whole wave function but rather only on the marginals. Not every collection of…

Sekine quantum groups are a family of finite quantum groups. The main result of this paper is to compute all the idempotent states on Sekine quantum groups, which completes the work of Franz and Skalski. This is achieved by solving a…

We construct a one parameter deformation of the group of $2\times 2$ upper triangular matrices with determinant 1 using the twisting construction. An interesting feature of this new example of a locally compact quantum group is that the…

The concept of weak invariants is examined in the thermodynamic context. Discussions are made about the temporally-local equilibrium states, corrections to them, and isoenergetic processes based on the quantum master equations of the…

We work in the density model of random groups. We prove that they satisfy an isoperimetric inequality with sharp constant $1-2d$ depending upon the density parameter $d$. This implies in particular a property generalizing the ordinary $C'$…

Haar measure is a fundamental structure in harmonic analysis on locally compact groups. Its existence reflects the compatibility between topology and the associative algebraic structure of groups. In this paper we propose a framework for…

The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.

For selected classes of quantum mechanical Hamiltonians a canonical association of a decay semigroup is presented. The spectrum of the generator of this semigroup is a pure eigenvalue spectrum and it coincides with the set of all…

We develop the theory of quasi--invariant (resp. strongly quasi--invariant) states under the action of a group $G$ of normal $*$--automorphisms of a $*$--algebra (or von Neumann alegbra) $\mathcal{A}$. We prove that these states are…

Let $A$ be a separable simple exact ${\cal Z}$-stable $C^*$-algebra. We show that the unitay group of ${\tilde A}$ has the cancellation property. If $A$ has continuous scale, the Cuntz semigroup of $\tilde A$ has the strict comparison…