A noncommutative space is considered the position operators of which satisfy the commutativity relations of a Lie algebra. The basic tools for calculation on this space, including the product of the fields, inner product and the proper measure for integration are derived. Some general aspects of perturbative field theory calculations on this space are also discussed. Among the features of such models is that they are free from ultraviolet divergences (and hence free from UV/IR mixing as well), if the group is compact. The example of the group SO(3) or SU(2) is investigated in more detail.

By taking the interacting spinor-scalar theory on the AdS d+1 space we calculate the boundary CFT correlation functions using AdS/CFT correspondence.

Multispecies reaction-diffusion systems, for which the time evolution equations of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time dependence of the average densities in these cases are also studied. For the general case, the large-time behavior of the average densities has also been obtained.