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Information × Registration Number 0226U000211, (0125U002856) , R & D reports Title Classification of subalgebras of Lie algebras and symmetry analysis of submodels of the system of Nizhnik equations popup.stage_title Дослідження алгебраїчних і геометричних властивостей підмоделей системи рівнянь Нижника та опис максимальних підалгебр алгебр Лі всіх диференціювань алгебри поліномів від багатьох змінних Head Vinnichenko Oleksandra O., Доктор філософії Registration Date 06-01-2026 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description1 The purpose of the work is to perform a symmetry analysis of submodels of the system of Nizhnik equations, in particular the Boiti–Leon–Manna–Pempinelli equation, using various algebraic methods, and to investigate the maximal subalgebras of the Lie algebra of all derivations of the polynomial algebra in several variables. popup.description2 Research report: 38 pages, 2 sections, 16 references. Keywords: SYMMETRIES OF DIFFERENTIAL EQUATIONS, SYMMETRY PSEUDOGROUPS, LIE REDUCTIONS, EXACT SOLUTIONS, LIE ALGEBRAS, ALGEBRAS OF DERIVATIONS, SUBALGEBRAS. The object of research is submodels of the system of Nizhnik equations and subalgebras of Lie algebra. The aim of stage I of the research project is the analysis of symmetry structures of submodels of the system of Nizhnik equations, in particular the Boiti–Leon–Manna–Pempinelli equation, their algebraic and geometric properties, and the proof of maximality of certain distinguished subalgebras of Lie algebras. Research methods are methods of the theory of Lie algebras and differential equations, standard methods of differential algebra, the infinitesimal Lie method, various versions of the algebraic method for constructing point-symmetry (pseudo)group of system of differential equations, and the representation theory of semisimple Lie algebras for proving the maximality of subalgebras of Lie algebras. Within the first stage “Investigation of algebraic and geometric properties of submodels of the system of Nizhnik equations and description of maximal subalgebras of Lie algebras of all derivations of the algebra of polynomials in several variables” of the research project, a study of submodels of the system of Nizhnik equations was carried out, in particular the (1+2)-dimensional integrable Boiti–Leon–Manna–Pempinelli equation. Maximal Lie invariance pseudoalgebras of the equations and systems under consideration were constructed using algebraic methods; megaideals were identified and point-symmetry pseudogroups were computed. Maximal subalgebras of Lie algebras of all derivations of the algebra of polynomials in several variables were investigated. The maximality of certain subalgebras selected on geometric grounds was proved using methods of the representation theory of semisimple Lie algebras. Product Description popup.authors Yevhenii Y. Chapovskyi Oleksandra O. Vinnichenko popup.nrat_date 2026-01-06 Close