On *-representations of algebras associated with Dynkin graph E₆

Abstract:
We present a complete description of non-degenerate *-representations of *-algebras associated with Dynkin graph E₆ introduced recently by S. Krugljak, S. Popovych and Yu. Samoylenko and related to spectral problem abot possible spectra of three Hermitian operators such that A + B = C. We also prove rigidity conjecture abot such representations.