  We investigate the structure of an infinite-dimensional symmetry of the
four-dimensional K\"ahler WZW model, which is a possible extension of the
two-dimensional WZW model. We consider the SL(2,R) group and, using the Gauss
decomposition method, we derive a current algebra identified with a
two-toroidal Lie algebra, a generalization of the affine Kac-Moody algebra. We
also give an expression of the energy-momentum tensor in terms of currents and
extra terms.
