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Information × Registration Number 0222U001762, 0119U100373 , R & D reports Title An investigation of algebraic structures with natural restrictions and some questions of quantum mechanics popup.stage_title Head Kurdachenko Leonid А., Доктор фізико-математичних наук Registration Date 02-02-2022 Organization Oles Honchar Dnipro National University popup.description2 The objects of study are algebras (Lie algebras and Leibniz algebras and other types of algebras), groups, some types of linear groups and modules over group rings. The aim of work is to build a general theory of Leibniz algebras, in particular the theory of generalized nilpotent and generalized solvable Leibniz algebras. Study of the influence on the structure of a group of restrictions arising from various important numerical invariants. Study of the influence of some norms (including non-Abelian) on the structure of the group. Development of the theory of modules over group rings, as well as over Leibniz algebras. In addition, the work aims to find an effective method for taking into account the orthogonality of quantum states and comparative analysis with existing methods of quantum mechanics. Research methods -modern methods of theory of groups, rings and modules. As a result of research the description of Leibniz algebras with restrictions on some systems of their subalgebras is received. An analysis of approach to the study of Leibniz algebras, which is based on the concept of anticenter and antinilpotency, is made. The Leibniz algebras of dimension 3 are described. Describe the structure of some groups with restrictions on the systems of their subgroups. Criteria for the primitiveness of group algebras of some classes of locally solvable groups are obtained. Analogues of Hall's theorem for infinitely dimensional linear groups with restrictions related to sectional rank are obtained. Non-periodic generalized solvable groups whose cyclic subgroups GNA subgroups are described. Finite generated linear groups of finite rank, which have exact irreducible primitive images over the field of characteristic 0, are studied. Analogues of Bear's theorem for Poisson algebras are obtained.Scope of use: in teaching algebraic special courses and for in-depth training of graduate students on research; in further research on group theory, modules of Lie and Leibniz algebras. Product Description popup.authors Hlushkov Vitaliy M. Kurdachenko Leonid А. Pypka Oleksandr O. Tushev Anatoliy V. Chupordia Vasyl A. Yashchuk Viktoriia S. popup.nrat_date 2022-03-09 Close