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

  • S. A. Kruhlyak
  • I. V. Livins'kyi Iн-т математики НАН України, Київ

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.
Published
25.08.2010
How to Cite
KruhlyakS. A., and Livins’kyiI. V. “Regular Orthoscalar Representations of the Extended Dynkin Graph $\widetilde{E}_8$ and ∗-Algebra Associatedwith It”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, no. 8, Aug. 2010, pp. 1044–1062, https://umj.imath.kiev.ua/index.php/umj/article/view/2936.
Section
Research articles