Related papers: The Lamplighter Group
In this note we show that the known relation between double groupoids and matched pairs of groups may be extended, or seems to extend, to the triple case. The references give some other occurrences of double groupoids.
We study and relate certain actions and extensions involving 2-groups.
We characterize and classify quantum correlations in two-fermion systems having 2K single-particle states. For pure states we introduce the Slater decomposition and rank (in analogy to Schmidt decomposition and rank), i.e. we decompose the…
We prove that if a group generated by a bireversible Mealy automaton contains an element of infinite order, its growth blows up and is necessarily exponential. As a direct consequence, no infinite virtually nilpotent group can be generated…
It is well known that different preparations of a mixed state cannot be distinguished by a measurement of that state. Yet we show that some other experiments let us make this distinction despite a very general belief that this would not be…
Different group structures which underline the integrable systems are considered. In some cases, the quantization of the integrable system can be provided with substituting groups by their quantum counterparts. However, some other group…
We analyze special class of bipartite states - so called Bell diagonal states. In particular we provide new examples of bound entangled Bell diagonal states and construct the class of entanglement witnesses diagonal in the magic basis.
A multiparticle quantum superposition state has been generated by a novel phase-selective parametric amplifier of an entangled two-photon state. This realization is expected to open a new field of investigations on the persistence of the…
It is shown that the coset lattice of a finite group has shellable order complex if and only if the group is complemented. Furthermore, the coset lattice is shown to have a Cohen-Macaulay order complex in exactly the same conditions. The…
We consider the method of entanglement witness operator to verify genuine multipartite entanglement for single-particle W states involving N parties. In particular, linear optical schemes using photo detectors and beam splitters are…
We provide a categorical notion called uncertain bisimilarity, which allows to reason about bisimilarity in combination with a lack of knowledge about the involved systems. Such uncertainty arises naturally in automata learning algorithms,…
Besides the oscillator group, there is another four-dimensional non-abelian solvable Lie group that admits a bi-invariant pseudo-Riemannian metric. It is called split oscillator group (sometimes also hyperbolic oscillator group or Boidol's…
We show that a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank has Prufer 2-rank at most two. This article covers the signalizer functor theory and identifies the groups of Lie…
We study the near action of the group PC of piecewise continuous self-transformations of the circle. Elements of this group are only defined modulo indeterminacy on a finite subset, which raises the question of realizability: a subgroup of…
We give a condition for an almost constant-type manifold to be a constant-type manifold, and holomorphic and $R$-invariant submanifolds of almost Hermitian manifolds are studied. Generalizations of some results in [5] are given.
The knapsack problem is a classic optimisation problem that has been recently extended in the setting of groups. Its study reveals to be interesting since it provides many different behaviours, depending on the considered class of groups.…
It is shown that any finite group $A$ is realizable as the automizer in a finite perfect group $G$ of an abelian subgroup whose conjugates generate $G$. The construction uses techniques from fusion systems on arbitrary finite groups, most…
The concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie group. For the simplest Lie groups the system of coherent states is constructed and its features are investigated.
Let $A$ be a finite set and $G$ a group. A closed subset $X$ of $A^G$ is called a subshift if the action of $G$ on $A^G$ preserves $X$. If $K$ is a closed subset of $A^G$ such that membership in $K$ is determined by looking at a fixed…
Twin observables, i.e. opposite subsystem observables A+ and A- that are indistinguishable in measurement in a given mixed or pure state W, are investigated in detail algebraicly and geometrically. It is shown that there is a far-reaching…