XXXVII Workshop on Geometric Methods in Physics 1-7.07.2018
VII School on Geometry and Physics 25-29.06.2018

Francesco Toppan

Quasi-nonassociativity from an exceptional spectrum-generating superalgebra.

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.

Event sponsored by:
of Bialystok
University of Bialystok

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