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Information × Registration Number 0224U000961, 0123U102992 , R & D reports Title Representations and cohomologies of groups and semigroups popup.stage_title Head Plakosh Andriiana I., Кандидат фізико-математичних наук Registration Date 15-01-2024 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description2 Object of research: integer representations of group A_4. Purpose of the work: To study the general properties of representations and cohomologies of crossed group rings. Research methods. The results on images and cohomologies known for ordinary group rings are used. Main priority results. - We establish a connection between the representations and cohomologies of crossed group rings and the representations and cohomologies of coefficient rings. The results on representations and cohomology known for ordinary group rings are transferred to crossed group rings and applied to semi-direct products of groups, in particular, to the alternative group A_4. We describe all the irreducible integer representations of group A_4 and explain the ambiguity of the irreducible representation decomposition. Predictive proposals for the development of the object of study. These results can be applied in scientific institutions engaged in the study and application of algebraic and topological structures, in particular, at the Taras Shevchenko National University of Kyiv, the Institute of Applied Problems of Mathematics and Mechanics named after Y. P. Pidstryhach Institute of Applied Problems of Mathematics and Mechanics, Uzhhorod National University, Ivan Franko National University of Lviv, etc. Keywords: representation, cohomology, group, semigroup, lattice, group ring, crystallographic group, Chernikov group Product Description popup.authors popup.nrat_date 2024-01-15 Close