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Information × Registration Number 0224U001885, 0122U001222 , R & D reports Title An investigation and description of the structure of important types of algebras, modules and groups and some questions of quantum mechanics popup.stage_title Head Kurdachenko Leonid А., Доктор фізико-математичних наук Registration Date 01-02-2024 Organization Oles Honchar Dnipro National University popup.description2  The objects of research are Leibniz algebras, groups, modules and braces. The purpose of the work is to obtain a description of the structure and important characteristics of the studied algebraic structures with the application of natural constraints on important systems of their substructures and factor structures and the application of quantum mechanics tools to solving density functional theory problems. Research methods are modern methods of the theory of algebras, groups, modules and braces. A description of automorphism groups and algebras of derivations of 3-dimensional Leibniz algebras, ideally finite Leibniz algebras, groups with pronormal and subnormal deviation, groups and modules without perfect factors, groups by the properties of their norms of decomposable subgroups, nilpotent according to Smoktunovych braces was obtained. The results are new and correspond to the world level of scientific research. The obtained results are implemented in the educational process. They are a significant addition to the corresponding algebraic courses, and also have a positive effect on the high-quality in-depth training of graduate students on the subject of research work. The results are directly related to research works devoted to research within the theory of Leibniz algebras, groups, modules and braces, which are carried out at universities in Ukraine, USA, Italy, Spain, etc. The significance of the obtained results lies in the tangible advantages compared to the results of researchers working within general algebra. The obtained results indicate the prospects of further research within the limits of the theories of groups, algebras, modules and braces, which can be significantly developed in the future due to the new results obtained within the scope of this research work. Product Description popup.authors Kurdachenko Leonid А. Lukashova Tetiana D. Pypka Oleksandr O. popup.nrat_date 2024-02-01 Close