2017
Том 69
№ 9

All Issues

Regular orthoscalar representations of the extended Dynkin graph $\widetilde{E}_8$ and ∗-algebra associatedwith it

Kruhlyak S. A., Livins'kyi I. V.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 8, pp 1213-1233.

Citation Example: Kruhlyak S. A., Livins'kyi I. V. Regular orthoscalar representations of the extended Dynkin graph $\widetilde{E}_8$ and ∗-algebra associatedwith it // Ukr. Mat. Zh. - 2010. - 62, № 8. - pp. 1044–1062.

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