Geodesic
An optimal system of one-dimensional subalgebras for the symmetry algebra of three-dimensional equations of the perfect plasticity
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 196-220

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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.
Keywords: theory of plasticity, isostatic coordinate, symmetry group, symmetry algebra, optimal system, algorithm.
Mots-clés : subalgebra 
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V. A. Kovalev; Yu. N. Radaev. An optimal system of one-dimensional subalgebras for the symmetry algebra of three-dimensional equations of the perfect plasticity. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 196-220. http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a26/