Ukrainian Mathematical Journal

, Volume 62, Issue 8, pp 1213–1233 | Cite as

Regular orthoscalar representations of the extended Dynkin graph \( {\tilde{E}_8} \) AND ∗-algebra associatedwith it

  • S. A. Kruhlyak
  • I. V. Livins’kyi

We obtain a classification of regular orthoscalar representations of the extended Dynkin graph \( {\tilde{E}_8} \) with special character. Using this classification, we describe triples of self-adjoint operators A, B, and C such that their spectra are contained in the sets {0, 1, 2, 3, 4, 5}, {0, 2, 4}, and {0, 3}, respectively, and the equality A + B + C = 6I is true.


Hilbert Space Unitary Transformation Zero Element Imaginary Root Indecomposable Representation 
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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • S. A. Kruhlyak
    • 1
  • I. V. Livins’kyi
    • 2
  1. 1.Institute of Mathematics, Ukrainian National Academy of SciencesKyivUkraine
  2. 2.Shevchenko Kyiv National UniversityKyivUkraine

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