Related papers: Characterizing Transfer Systems for Non-Abelian Gr…

Exceptional points, the spectral degeneracy points in the complex parameter space, are fundamental to non-Hermitian quantum systems. The dynamics of non-Hermitian systems in the presence of exceptional points differ significantly from those…

Transfer systems are combinatorial objects which classify $N_\infty$ operads up to homotopy. By results of A. Blumberg and M. Hill, every transfer system associated to a linear isometries operad is also saturated (closed under a particular…

Let $G$ be a finite, non-abelian group of the form $G = A N$, where $A \leq G$ is abelian, and $N \trianglelefteq G$ is cyclic. We prove that the commuting graph $\Gamma(G)$ of $G$ is either a connected graph of diameter at most four, or…

In this paper, we present a unifying analytical framework for identifying conditions for transport effects such as reflectionless and transparent transport, lasing, and coherent perfect absorption in non-Hermitian nonreciprocal systems…

Finite (or Discrete) Fourier Transforms (FFT) are essential tools in engineering disciplines based on signal transmission, which is the case in most of them. FFT are related with circulant matrices, which can be viewed as group matrices of…

Let $G$ be a graph whose edges are each assigned one of the $m$-colours $1, 2, \ldots, m$, and let $\Gamma$ be a subgroup of $S_m$. The operation of switching at a vertex $x$ with respect $\pi \in \Gamma$ permutes the colours of the edges…

Properties of a given symmetry group G are very important in investigation of a physical system invariant under its action. In the case of finite spin systems (magnetic rings, some planar macromolecules) the symmetry group is isomorphic…

Multi-Higgs models equipped with global symmetry groups, either exact or softly broken, offer a rich framework for constructions beyond the Standard Model and lead to remarkable phenomenological consequences. Knowing all the symmetry…

We introduce lattice gauge theories which describe three-dimensional, gapped quantum phases exhibiting the phenomenology of both conventional three-dimensional topological orders and fracton orders, starting from a finite group $G$, a…

We describe the reduced formal context of the lattice of saturated transfer systems on a finite abelian group. As an application, we compute that there are 13,784,538,270,571 saturated transfer systems on the elementary abelian group…

In this paper, we initiate the study of spectrum of the commuting graphs of finite non-abelian groups. We first compute the spectrum of this graph for several classes of finite groups, in particular AC-groups. We show that the commuting…

The study of perfect state transfer on graphs has attracted a great deal of attention during the past ten years because of its applications to quantum information processing and quantum computation. Perfect state transfer is understood to…

Perfect nonlinear functions from a finite group $G$ to another one $H$ are those functions $f: G \rightarrow H$ such that for all nonzero $\alpha \in G$, the derivative $d_{\alpha}f: x \mapsto f(\alpha x) f(x)^{-1}$ is balanced. In the case…

We show that the functor which assigns to an A-infinity morphism between isotopy classes of A-infinity algebras whose linear part is a chain homotopy equivalence its underlying chain map is a discrete Grothendieck bifibration. We then…

Higher form symmetry, one of the generalized symmetries, primarily involves the action of abelian groups. This is, due to the topological nature of symmetry defect operators. In this study, we extend the vector space (or vector bundle) in…

We provide a complete description of the model category structures on the nonmodular lattice $N_5$. Furthermore we explain how these model category structures are related to each other via Bousfield localization. This work heavily relies on…

The key information of a model category structure on a poset is encoded in a transfer system, which is a combinatorial gadget, originally introduced to investigate homotopy coherence structures in equivariant homotopy theory. We describe…

Let $G$ be a non-abelian group and $Z(G)$ be the center of $G$. The non-commuting graph $\Gamma_G$ associated to $G$ is the graph whose vertex set is $G\setminus Z(G)$ and two distinct elements $x,y$ are adjacent if and only if $xy\neq yx$.…

Let $f:X\to Y$ be a finite ramified Galois covering of algebraic varieties defined over the complex numbers. In this paper, we prove some structure theorems for such coverings in the case that the non-abelian Galois group of the cover is…

In this paper we study non-abelian extensions of a Lie group $G$ modeled on a locally convex space by a Lie group $N$. The equivalence classes of such extension are grouped into those corresponding to a class of so-called smooth outer…