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Information × Registration Number 0213U001025, 0112U005849 , R & D reports Title Representation of groups, algebras, invariant theory and their aplication popup.stage_title Head Bodnarchuk Yuriy Victorovich, Registration Date 09-01-2013 Organization National University of "Kyiv-Mohyla Academy" popup.description2 The method of obtaining identities between special polynomials (Apel's polynomials in particular ), which play an important role in theoretic physics is proposed. The method based on invariant theory and representation theory of Lie algebras, which in some cases make possible to get a full description of kernels of locally nilpotent derivation (LND).It is shown how the problem of description of root LND reduced to description LND, which are root elements in the correspondent Lie algebra. The structure of the universal envelope Lie algebra of unitriangular polynomial (in three variables) derivations is ascertained. It turns out that its localization over the center is a generalized Weil algebra. LND with some restrictions on Newton polyhedron were investigated, in particular, flat LND with two elementary monomial derivations. The methods of theory of LND was applied to studying invariant transformations of sequences of integers and classification problems for algebraic curves as well. It is proven that there exists a unique realization of quasi- boson operators of birth and annihilation by algebra of deformed oscillator, when the structure function of deformation is square-nonlinear under the operator of a number of particles. There was deduced virial expansion for state equation of p,q - Bose gas and several virial coefficients were calculated. Product Description popup.authors Бедратюк Л. П. Боднарчук Ю. В. Качурик І. І. Прокоф'єв П. Г. popup.nrat_date 2020-04-02 Close