  The paper is devoted to group analysis of the spatially homogeneous and
isotropic Boltzmann equation with a source term. In fact, the Fourier transform
of the Boltzmann equation with respect to the molecular velocity variable is
considered. Using a particular class of solutions, the determining equation for
the admitted Lie group is reduced to a partial differential equation for the
source function. The latter equation is analyzed by an algebraic method. A
complete group classification of the Fourier transform of the Boltzmann
equation is given. All invariant solutions of this equation are also presented
in the paper.
