Three-particle Calogero model: Supertraces and ideals on the observables algebra

The associative observables superalgebra of the three-particle Calogero model giving all its wave functions via the standard Fock procedure has two independent supertraces. When the coupling constant $\nu$ is $n\pm1/3$ or $n+1/2$, the existence of two independent supertraces leads to the existence of a nontrivial two-sided ideal in the observables superalgebra for any integer $n$.