Exceptional Lie (super)algebras are derived from octonions. I present the Calogero-deformed quantum oscillator derived from the spectrum generating superalgebra F(4). Its spectrum is a direct sum of F(4) lowest weight representations. This system is a unique example of “quasi-nonassociativity”. This means, in particular, that the Calogero coupling constants are determined in terms of the octonionic structure constants. The Hilbert space is a 16-ple of square integrable functions.
This talk is based on the paper arXiv:1711.02923[math-ph], published in J. Math. Phys. 59, 022101 (2018) in collaboration with N. Aizawa and Z. Kuznetsova.