This paper describes a new algorithm for determining all discrete contact symmetries of any differential equation whose Lie contact symmetries are known. The method is constructive and is easy to use. It is based upon the observation that the adjoint action of any contact symmetry is an automorphism of the Lie algebra of generators of Lie contact symmetries. Consequently, all contact symmetries...

Suppressing Z2-monopoles shifts the line of deconfinement transitions in the coupling plane of the SU(2) lattice gauge theory with a mixed Villain form of action but it still continues to behave also like the bulk transition line. Separate deconfinement and bulk phase transitions are found on the same lattice, suggesting the two to be indeed coincident at higher adjoint couplings. Universality ...

A posteriori estimation of the numerical error sensitivity to the local truncation error is addressed using adjoint model endowed with the information on the error field. The numerical error is estimated from the solution of the linear tangent model (LTM) or from a Richardson extrapolation. The local truncation error used in the LTM is obtained by the action of a high order finite-difference st...

We utilize group-theoretical methods to develop a matrix representation of differential operators that act on tensors of any rank. In particular, we concentrate on the matrix formulation of the curl operator. A self-adjoint matrix of the curl operator is constructed and its action is extended to a complex plane. This scheme allows us to obtain properties, similar to those of the traditional cur...

The adjoint action of a nite group of Lie type on its Lie algebra is studied. A simple formula is conjectured for the number of split semisimple orbits of a given genus. This conjecture is proved for type A, and partial results are obtained for other types. For type A a probabilistic interpretation is given in terms of Solomon's descent algebra and card shu ing. 3

We define a semi-Hopf algebra which is more general than a Hopf algebra. Then we construct the supersymmetry algebra via the adjoint action on this semi-Hopf algebra. As a result we have a supersymmetry theory with quantum gauge group, i.e., quantised enveloping algebra of a simple Lie algebra. For the example, we construct the Lagrangian N =1 and N =2 supersymmetry. ∗email : [email protected] 1

For SU(2) lattice gauge theory with the fundamental-adjoint action an efficient heat-bath algorithm is not known so that one had to rely on Metropolis simulations supplemented by overrelaxation. Implementing a novel biased Metropolis-heat-bath algorithm for this model, we find improvement factors in the range 1.45 to 2.06 over conventionally optimized Metropolis simulations. If one optimizes fu...

In this paper, we give a proof of the equivalence of N = 1 SO/Sp gauge theories deformed from N = 2 by the superpotential of adjoint field Φ and the dual type IIB supersting theory on CY threefold geometries with fluxes and orientifold action after geometric transition. Furthermore, by relating the geometric picture to the matrix model, we show the equivalence among the field theory and the cor...

A unified extension of the gradient flows and the double bracket equations of ChuDriessel and Brockett is obtained in the frame work of reductive Lie groups. We examine the gradient flows on the orbit in the Cartan subspace of a reductive Lie algebra, under the adjoint action. The results of Chu-Driessel and Brockett are corresponding to the reductive groups GL(n,R) and O(p, q).

n An), and |a| ∈ Z denotes the grading. The bracket and differential are required to respect the grading, in that for homogeneous elements, |[a, b]| = |a| + |b| while |∂a| = |a| − 1. The adjoint action of A on itself is given by ade(a) = [e, a] and acts on the grading by ade : An−→An+|e|. In this notation (2) and (3) can be rewritten as • (2) (Jacobi identity) ad[a,b] = [ada, adb] • (3) (Leibni...