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.