3-particle Calogero Model: Supertraces and Ideals on the Algebra of Observables

The associative superalgebra of observables of 3-particle Calogero model giving all wavefunctions of the model via standard Fock procedure has 2 independent supertraces. It is shown here that when the coupling constant u is equal to n+1/3, n-1/3 or n+1/2 for any integer n the existence of 2 independent supertraces leads to existence of nontrivial two-sided ideal in the superalgebra of observables.