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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 8, pp. 1044–1062, August, 2010.
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Kruhlyak, S.A., Livins’kyi, I.V. Regular orthoscalar representations of the extended Dynkin graph \( {\tilde{E}_8} \) AND ∗-algebra associatedwith it. Ukr Math J 62, 1213–1233 (2011). https://doi.org/10.1007/s11253-011-0425-z
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DOI: https://doi.org/10.1007/s11253-011-0425-z