@article{Kruhlyak_Livins’kyi_2010, title={Regular orthoscalar representations of the extended Dynkin graph $\widetilde{E}_8$ and ∗-algebra associatedwith it}, volume={62}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2936}, abstractNote={We obtain a classification of regular orthoscalar representations of the extended Dynkin graph $\widetilde{E}_8$ 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.}, number={8}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Kruhlyak, S. A. and Livins’kyi, I. V.}, year={2010}, month={Aug.}, pages={1044–1062} }