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  • Savchuk, Yuri (Луганский национальный университет им. Т. Шевченко, 2004)
    We describe the C -algebra generated by four orthogonal projections p1, p2, p3, p4, satisfying the linear relation p1 + p2 + p3 + p4 = 2I. The simplest realization by 2 × 2-matrixfunctions over the sphere S2 is given.
  • Vlasenko, Masha (Луганский национальный университет им. Т. Шевченко, 2004)
  • Drozd, Yuriy A.; Kubichka, Eugene A. (Луганский национальный университет им. Т. Шевченко, 2004)
    We consider the dimensions of finite type of rep- resentations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimen- sion. We give a criterion for ...
  • Mellit, Anton (Луганский национальный университет им. Т. Шевченко, 2004)
    We consider the algebras ei (Q)ei, where (Q) is the deformed preprojective algebra of weight and i is some vertex of Q, in the case where Q is an extended Dynkin diagram and lies on the hyperplane orthogonal to the ...
  • Jushenko, Ekaterina (Луганский национальный университет им. Т. Шевченко, 2004)
    In this paper we study affine Coxeter groups. We show how to construct decompositions of the investigated groups into semi-direct products. We use this to give the complete list of irreducible representations of affine ...
  • Mazorchuk, Volodymyr (Луганский национальный университет им. Т. Шевченко, 2004)
    In this survey we discuss the results on the fini- tistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
  • Chapovsky, Yu. A.; Kalyuzhnyi, A. A.; Podkolzin, G. B. (Луганский национальный университет им. Т. Шевченко, 2004)
    For the cocycle bicrossed product construction applied to a locally compact group and its two subgroups, we give a simple description of the group of the corresponding extensions in terms of the second cohomology group ...
  • Kyrychenko, A. A.; Samoˇılenko, Yu. S. (Луганский национальный университет им. Т. Шевченко, 2004)
  • Bondarenko, Vitalij M. (Луганский национальный университет им. Т. Шевченко, 2004)
    Let denote an extended Dynkin diagram with vertex set 0 = {0, 1, . . . , n}. For a vertex i, denote by S(i) the set of vertices j such that there is an edge joining i and j; one assumes the diagram has a unique vertex ...
  • Timoshin, Anatoliy S. (Луганский национальный университет им. Т. Шевченко, 2004)
    In the space of irreducible unitary representations of a linear group over an algebra of type e A2 an open dense subset of representations in the general position is singled out. This set is identified, up to simple ...
  • Frisk, Anders (Луганский национальный университет им. Т. Шевченко, 2004)
    We study the class of standardly stratified alge- bras introduced by Cline, Parshall and Scott, and its subclass of the so-called weakly properly stratified algebras, which generalizes the class of properly stratified ...
  • Popovych, Stanislav; Turowska, Lyudmila (Луганский национальный университет им. Т. Шевченко, 2004)
    The problem of unitarization of representations of algebras generated by idempotents with linear relations is studied. Construction of non-unitarizable representations for some subintervals of continuous spectrum is ...

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