Related papers: The Frucht property in the quantum group setting

A formulation of quantum mechanics based on replacing the general unitary group by finite groups is considered. To solve problems arising in the context of this formulation, we use computer algebra and computational group theory methods.

We describe the full automorphism group of the power (di)graph of a finite group. As an application, we solve a conjecture proposed by Doostabadi, Erfanian and Jafarzadeh in 2013.

We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that…

Building on work of Farb and the second author, we prove that the group of automorphisms of the fine curve graph for a surface is isomorphic to the group of homeomorphisms of the surface. This theorem is analogous to the seminal result of…

We classify the finite quasisimple groups whose commuting graph is perfect and we give a general structure theorem for finite groups whose commuting graph is perfect.

If G is a (connected) complex Lie Group and Z is a generalized flag manifold for G, the the open orbits D of a (connected) real form G_0 of G form an interesting class of complex homogeneous spaces, which play an important role in the…

For a classical group $G$ over a field $F$ together with a finite-order automorphism $\theta$ that acts compatibly on $F$, we describe the fixed point subgroup of $\theta$ on $G$ and the eigenspaces of $\theta$ on the Lie algebra…

The quantum field algebra of real scalar fields is shown to be an example of infinite dimensional quantum group. The underlying Hopf algebra is the symmetric algebra S(V) and the product is Wick's normal product. Two coquasitriangular…

We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…

Star products on the classical double group of a simple Lie group and on corresponding symplectic grupoids are given so that the quantum double and the "quantized tangent bundle" are obtained in the deformation description. "Complex"…

This paper gives a new explicit construction of the $\mathbb{Q}$-algebraic hull for virtually solvable groups $\Gamma$ of finite abelian ranks, taking into account the spectrum $S$ of the group $\Gamma$. As an application, we make a…

Let $\Gamma$ be a simple undirected graph on a finite vertex set and let $A$ be its adjacency matrix. Then $\Gamma$ is {\it singular} if $A$ is singular. The problem of characterising singular graphs is easy to state but very difficult to…

We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.

We describe a group theoretic condition which ensures that any cellular action of a group satisfying this condition on a CAT(0) cube complex has a global fixed point. In particular, we show that this fixed point criterion is satisfied by…

Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…

We establish a quantum Galois correspondence for compact Lie groups of automorphisms acting on a simple vertex operator algebra.

In this paper, we consider the probability that a randomly chosen automorphism of a finite group fixes a randomly chosen element of a subgroup of that group. We obtain several new results as well as generalizations and improvements of some…

The recently introduced A-homotopy groups for graphs are investigated. The main concern of the present article is the construction of an infinite cell complex, the homotopy groups of which are isomorphic to the A-homotopy groups of the…

We compute the $ K $-theory of quantum automorphism groups of finite dimensional $ C^* $-algebras in the sense of Wang. The results show in particular that the $ C^* $-algebras of functions on the quantum permutation groups $ S_n^+ $ are…

A finite graph $\Gamma$ is called $G$-symmetric if $G$ is a group of automorphisms of $\Gamma$ which is transitive on the set of ordered pairs of adjacent vertices of $\Gamma$. We study a family of symmetric graphs, called the unitary…