On group classification of the spatially homogeneous and isotropic Boltzmann equation with sources II

•The algebraic approach for the group classification is applied.•Complete group classification of the equation for the generating moment function is presented.•The approach differs from the approach used in previous paper.

A previous paper by the authors (Grigoriev and Meleshko, 2012 [4]) was devoted to group analysis of the equation for the power moment generating function of a solution of the Boltzmann kinetic equation with sources. An approach developed earlier by Grigoriev and Meleshko (1986 [2]) was employed for finding the admitted Lie group. This approach allowed to correct Nonenmacher׳s results (1984, [1]) and to perform a partial group classification of the considered equation with respect to a source function. The present paper completes this group classification by an efficient algebraic method.