In this note we discuss the structure of systems of coupled cells (which we view as systems of ordinary differential equations) where symmetries of the system are obtained through the group G of global permutations of the cells and the group L of local internal symmetries of the dynamics in each cell. We show that even when the cells are assumed to be identical with identical coupling, the way ...

We construct in a systematic way the complete Chevalley-Eilenberg cohomology at form degree two, three and four for the Galilei and Poincaré groups. The corresponding non-trivial forms belong to certain representations of the spatial rotation (Lorentz) group. In the case of two forms they give all possible central and non-central extensions of the Galilei group (and all non-central extensions o...

We present new computations of “intrinsic” symmetry groups for knots and links of 8 or fewer crossings. The standard symmetry group for a link is the mapping class group MCG(S, L) or Sym(L) of the pair (S, L). Elements in this symmetry group can (and often do) fix the link and act nontrivially only on its complement. We ignore such elements and focus on the “intrinsic” symmetry group of a link,...

In this paper we construct the supersymmetric tensor hierarchy of N=1, d=4 supergravity. We find some differences with the general bosonic construction of 4dimensional gauged supergravities. The global symmetry group of N = 1, d = 4 supergravity consists of three factors: the scalar manifold isometry group, the invariance group of the complex vector kinetic matrix and the U(1) R-symmetry group....

A configuration of particles confined to a sphere is balanced if they are in equilibrium under all force laws (that act between pairs of points with strength given by a fixed function of distance). It is straightforward to show that every sufficiently symmetrical configuration is balanced, but the converse is far from obvious. In 1957 Leech completely classified the balanced configurations in R...

We study the operator product expansion in the bosonic SU(2)0 and SUSY SU(2)2 WZNW models. We find that these OPEs contain both logarithmic operators and new conserved currents, leading to an extension of the symmetry group.

Lie symmetry group method is applied to study the Fisher-Kolmogorov equation. The symmetry group is given, and travelling wave solutions are obtained. Finally the conservation laws are determined.

We introduce a novel approach for symmetry breaking by dominance detection (SBDD). The essence of SBDD is to perform ‘dominance checks’ at each node in a search tree to ensure that no symmetrically equivalent node has been visited before. While a highly effective technique for dealing with symmetry in constraint programs, SBDD forces a major overhead on the programmer, of writing a dominance ch...