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  • C -algebra generated by four projections with sum equal to 2 
    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.
  • Description of the center of certain quotients of the Temperley-Lieb algebra of type e AN 
    Vlasenko, Masha (Луганский национальный университет им. Т. Шевченко, 2004)
  • Dimensions of finite type for representations of partially ordered sets 
    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 ...
  • Kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation 
    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 ...
  • On decompositions of affine Coxeter groups in semi-direct products 
    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 ...
  • On finitistic dimension of stratified algebras 
    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.
  • On the group of extensions for the bicrossed product construction for a locally compact group 
    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 ...
  • On the spectrum and spectrum multiplicities of a sum of orthogonal projections 
    Kyrychenko, A. A.; Samoˇılenko, Yu. S. (Луганский национальный университет им. Т. Шевченко, 2004)
  • On wildness of idempotent generated algebras associated with extended Dynkin diagrams 
    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 ...
  • Representations of linear groups over e A2-algebras 
    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 ...
  • Two-step tilting for standardly stratified algebras 
    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 ...
  • Unitarizable and non-unitarizable represenations of algebras generated by idempotents 
    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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