http://hdl.handle.net/123456789/4603 2026-04-15T20:15:23Z http://hdl.handle.net/123456789/4624 A new way to construct 1-singular Gelfand-Tsetlin modules Zadunaisky, P. We present a simplified way to construct the Gelfand-Tsetlin modules over gl(n, C) related to a 1-singular GT- tableau defined in [6]. We begin by reframing the classical construc- tion of generic Gelfand-Tsetlin modules found in [3], showing that they form a flat family over generic points of C( n 2) . We then show that this family can be extended to a flat family over a variety including generic points and 1-singular points for a fixed singular pair of entries. The 1-singular modules are precisely the fibers over these points. Zadunaisky P. A new way to construct 1-singular Gelfand-Tsetlin modules / P. Zadunaisky // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 1. - Рp. 180-193 2017-01-01T00:00:00Z http://hdl.handle.net/123456789/4623 Equivalence of Carter diagrams Stekolshchik, R. We introduce the equivalence relation ρ on the set of Carter diagrams and construct an explicit transformation of any Carter diagram containing l-cycles with l > 4 to an equivalent Carter diagram containing only 4-cycles. Transforming one Carter diagram Γ1 to another Carter diagram Γ2 we can get a certain intermediate diagram Γ′ which is not necessarily a Carter diagram. Such an intermediate diagram is called a connection diagram. The relation ρ is the equivalence relation on the set of Carter diagrams and connection diagrams. The properties of connection and Carter diagrams are studied in this paper. The paper contains an alternative proof of Carter’s classification of admissible diagrams. Stekolshchik R. Equivalence of Carter diagrams / R.Stekolshchik // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 1. - Рp.138-179 2017-01-01T00:00:00Z http://hdl.handle.net/123456789/4622 Dg algebras with enough idempotents, their dg modules and their derived categories M., Saorín We develop the theory dg algebras with enough idempotents and their dg modules and show their equivalence with that of small dg categories and their dg modules. We introduce the concept of dg adjunction and show that the classical covariant tensor- Hom and contravariant Hom-Hom adjunctions of modules over associative unital algebras are extended as dg adjunctions between categories of dg bimodules. The corresponding adjunctions of the associated triangulated functors are studied, and we investigate when they are one-sided parts of bifunctors which are triangulated on both variables. We finally show that, for a dg algebra with enough idempotents, the perfect left and right derived categories are dual to each other. Saorín M. Dg algebras with enough idempotents, their dg modules and their derived categories / M. Saorín // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 1. - Рp.62-137 2017-01-01T00:00:00Z http://hdl.handle.net/123456789/4621 On the representation type of Jordan basic algebras Kashuba, I.; Ovsienko, S.; Shestakov, I. A finite dimensional Jordan algebra J over a field k is called basic if the quotient algebra J/ Rad J is isomorphic to a direct sum of copies of k. We describe all basic Jordan algebras J with (Rad J) 2 = 0 of finite and tame representation type over an algebraically closed field of characteristic 0. Kashuba I. On the representation type of Jordan basic algebras / I.Kashuba, S.Ovsienko, I.Shestakov // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 1. - Рp. 47-61 2017-01-01T00:00:00Z