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Information × Registration Number 0225U001691, (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 Дослідження алгебр диференціювань та застосування квантової механіки до вирішення проблем функціоналу густини Head Kurdachenko Leonid А., Доктор фізико-математичних наук Registration Date 05-02-2025 Organization Oles Honchar Dnipro National University popup.description1 The aim of the research is to obtain a description of the structure and important characteristics of the studied algebraic structures using natural restrictions on important systems of their substructures and factor structures and the use of quantum mechanics tools to solve problems of density functional theory popup.description2 The aim of the work is to describe the structure and key characteristics of the studied algebraic structures by applying natural constraints on significant systems of their substructures and factor structures, as well as to apply quantum mechanics tools to address problems in density functional theory. Research methods – modern methods in the theory of algebras, groups, modules, and braces. The results of the research include a description of automorphism groups, semigroups of endomorphisms, and algebras of derivations of certain finite-dimensional Leibniz algebras considered over arbitrary fields; the establishment of properties of some modules over group rings; the classification of certain classes of groups where subnormal subgroups are free from contranormal subgroups; the identification of relationships between the center and the derived subalgebra in Leibniz 3-algebras and Poisson 3-algebras; the description of certain classes of groups with restrictions on the norms of abelian noncyclic subgroups; and the characterization of the structure and properties of some braces with constraints on subsystems of subbraces. The results are novel and align with the global standards of scientific research. The obtained results have been implemented in the educational process. They provide a substantial addition to relevant algebraic courses and contribute to the in-depth training of graduate students in the research field. These findings are directly related to research projects on Leibniz algebras, groups, modules, and braces conducted at universities in Ukraine, the USA, Italy, Spain, and beyond. The significance of the results lies in their considerable advantages compared to the findings of researchers working within the framework of general algebra. The obtained results highlight promising directions for further studies in the theories of groups, algebras, modules, and braces. Product Description popup.authors Kurdachenko Leonid А. Lukashova Tetiana D. Pypka Oleksandr O. popup.nrat_date 2025-02-05 Close