Abstract:
The present paper is devoted to a study of a natural $12$-dimensional symmetry algebra of the three-dimensional hyperbolic differential equations of the perfect plasticity, obtained by D. D. Ivlev in 1959 and formulated in isostatic coordinates. An optimal system of one-dimensional subalgebras constructing algorithm for the Lie algebra is proposed. The optimal system (total $187$ elements) is shown consisting of of a 3-parametrical element, twelve 2-parametrical elements, sixty six 1-parametrical elements and one hundred and eight individual elements.