Let G be a non-abelian group and let Z(G) be the center of G. Associate a graph ΓG (called noncommuting graph of G) with G as follows: Take G\Z(G) as the vertices of ΓG and join two distinct vertices x and y, whenever xy = yx. We want to explore how the graph theoretical properties of ΓG can effect on the group theoretical properties of G. We conjecture that if G and H are two non-abelian finit...

The original ideas about noncommuting coordinates are recalled. The connection between U(1) gauge fields defined on noncommuting coordinates and fluid mechanics is explained. Non-Abelian fluid mechanics is described. I The idea that configuration-space coordinates may not commute,

The original ideas about noncommuting coordinates are recalled. The connection between U(1) gauge fields defined on noncommuting coordinates and fluid mechanics is explained. The idea that configuration-space coordinates may not commute

Noncommuting spatial coordinates and fields can be realized in actual physical situations. Plane wave solutions to noncommuting photodynamics exhibit violaton of Lorentz invariance (special relativity). Feza Gursey Institute, Istanbul, Turkey – June 2001 “Symmetry Methods in Physics”, Yerevan, Armenia – July 2001 “CPT and Lorentz Symmetry II”, Bloomington, IN – August 2001 “Particles and String...

We discuss a general method of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. Starting from the commuting algebra in the conventional gauge, it is possible to obtain a noncommuting algebra in a nonstandard gauge. The change of variables relating the algebra in the two gauges is systematically deriv...

We discuss a method of revealing noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. Starting from the commuting algebra in the conventional gauge, it is possible to obtain a noncommuting algebra in a nonstandard gauge. The change of variables relating the algebra in the two gauges is systematically derived using gauge/reparametrisation transfo...

NCSOStools is a Matlab toolbox for • symbolic computation with polynomials in noncommuting variables; • constructing and solving sum of hermitian squares (with commutators) programs for polynomials in noncommuting variables. It can be used in combination with semidefinite programming software, such as SeDuMi, SDPA or SDPT3 to solve these constructed programs. This paper provides an overview of ...