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About $\ast$-representations of polynomial semilinear relations


In the present paper we study $\ast$-representations of semilinear relations with polynomial characteristic functions. For any finite simple non-oriented graph $\Gamma$ we construct a polynomial characteristic function such that $\Gamma$ is its graph. Full description of graphs which satisfy polynomial (degree one and two) semilinear relations is obtained. We introduce the $G$-orthoscalarity condition and prove that any semili ear relation with quadratic characteristic function and condition of $G$-orthoscalarity is $\ast$-tame. This class of relations contains, in particular, $\ast$-representations of $U_{q}(so(3)).$

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TitleAbout $\ast$-representations of polynomial semilinear relations
SourceMethods Funct. Anal. Topology, Vol. 15 (2009), no. 2, 168-176
MathSciNet   MR2553532
CopyrightThe Author(s) 2009 (CC BY-SA)

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P. V. Omel'chenko
Institute of Mathematics National Academy of Sciences of Ukraine, 3 Tereshchenkivska Str., Kiyv, 252601, Ukraine 

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P. V. Omel'chenko, About $\ast$-representations of polynomial semilinear relations, Methods Funct. Anal. Topology 15 (2009), no. 2, 168-176.


@article {MFAT523,
    AUTHOR = {Omel'chenko, P. V.},
     TITLE = {About $\ast$-representations of polynomial semilinear relations},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {15},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {168-176},
      ISSN = {1029-3531},
  MRNUMBER = {MR2553532},
       URL = {},

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