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Information × Registration Number 0214U001197, 0112U005849 , R & D reports Title Representation of groups, algebras, invariant theory and their aplication popup.stage_title Head Olijnyk Bogdana, Registration Date 23-01-2014 Organization National University of "Kyiv-Mohyla Academy" popup.description2 The project was aimed at development of new theoretical and computational methods in the theory of groups and algebras and their applications to combinatorial and spectral graph theory, design of algorithms for equivalent transformation of binary data, the usage of algebraic methods in the theory of special functions in theoretical physics. One of research areas of the modern algebra is the study of properties of different generalizations of well known classes of finite groups for an infinite-dimensional case. Classic examples of finite groups include so-called hyperoctahedral groups or groups of symmetries of the n-dimensional cube. These groups are realized as groups of full isometries of Hamming metric spaces. Hamming spaces have wide applications. They are used, in particular, in coding theory, theory of peer review, psychology, etc. There are different generalizations of Hamming spaces, namely the Hamming spaces of periodic sequences, the infinite-dimensional hypercube, the infinite-dimensional extended Hamming space, etc. Isometry groups of these spaces can be regarded as infinite-dimensional analogues of hyperoctahedral groups. The structure and representations of these groups are not well studied. In this direction we obtain some results. Namely, we constructed an isometric representation of the Hamming space of periodic sequences on the boundary of a rooted tree using spherically transitive automorphisms of this rooted tree. The normal structure of the infinite D-hyperoctahedral group is calculated. The representation of the infinite D-hyperoctahedral group by isometries of Hamming spaces of periodic sequences is described. The results are used to construct an algorithm for equivalent transformations of binary data. Product Description popup.authors Бендратюк Л. П. Дяченко С. М. Качурик І. І. Лебідь В. О. Олійник Б. В. popup.nrat_date 2020-04-02 Close