Related papers: Structures of Coincidence Symmetry Groups
For plane frameworks with reflection or rotational symmetries, where the group action is not necessarily free on the vertex set, we introduce a phase-symmetric orbit rigidity matrix for each irreducible representation of the group. We then…
Emergence of fundamental forces from gauge symmetry is among our most profound insights about the physical universe. In nature, such symmetries remain hidden in the space of internal degrees of freedom of subatomic particles. Here we…
We compute the full isometry group of any left invariant metric on a simply connected, non-unimodular Lie group of dimension three. As an application, we determine the index of symmetry of such metrics and prove that the singularities of…
Monodromy in analytic families of smooth complex surfaces yields groups of isotopy classes of orientation preserving diffeomorphisms for each family member X. For all deformation classes of minimal elliptic surfaces with p_g>q=0, we…
Spin glasses are quintessential examples of complex matter. Although much about their order remains uncertain, abstract models of them inform, e.g., the classification of combinatorial optimization problems, the magnetic ordering in metals…
We describe extension of the pyritohedral symmetry to 4-dimensional Euclidean space and present the group elements in terms of quaternions. It turns out that it is a maximal subgroup of both the rank-4 Coxeter groups W(F4) and W(H4)…
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…
Symmetries of finite Heisenberg groups represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. This short contribution presents extension of previous investigations to composite quantum systems…
We classify all groups which can occur as the topological symmetry group of some embedding of the Heawood graph in $S^3$.
A systematic procedure is developed for constructing fermion systems in discrete space-time which have a given outer symmetry. The construction is illustrated by simple examples. For the symmetric group, we derive constraints for the number…
We find an algorithmic procedure that enables to compute and to describe the structure of the isotropy subgroups of the group of complex orthogonal matrices with respect to the action of similarity on complex symmetric matrices. A key step…
The symmetry group structures of two dimensional coupled nonlinear Shr\"{o}dinger equations are considered. We first show that the equations admit infinite dimensional symmetry algebra as well as the corresponding symmetry group depending…
The purpose of this article is the study of the symmetries in a circular and linear harmonic oscillator chains system, and consequently use them as a means to find the eigenvalues of these configurations. Furthermore, a hidden…
The {\em topological symmetry group} of an embedding $\Gamma$ of an abstract graph $\gamma$ in $S^3$ is the group of automorphisms of $\gamma$ which can be realized by homeomorphisms of the pair $(S^3, \Gamma)$. These groups are motivated…
Coincidence site lattices of oblique planar lattices are algebraically characterized using as basic tool the Cartan-Dieudonn\'e theorem, that is, the decomposition of an orthogonal transformation as a product of reflections. The case of…
In gravity, breaking symmetry from a group G to a group H plays the role of describing geometry in relation to the geometry the homogeneous space G/H. The deep reason for this is Cartan's "method of equivalence," giving, in particular, an…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
The design and implementation of large sets of spatially-extended, gauge-invariant operators for use in determining the spectrum of baryons in lattice QCD computations are described. Group-theoretical projections onto the irreducible…
Let M denote either Euclidean or hyperbolic n-space, and let G be a discrete group of isometries of M, with the property that G respects and acts tile-transitively on a convex-polyhedral tesselation of M. Given an arbitrary base point p in…
The embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a…