Connection between the ideals generated by traces and by supertraces in the superalgebras of observables of Calogero models

S. E. Konstein, I. V. Tyutin

If $G$ is a finite Coxeter group, then symplectic reflection algebra $H:=H_{1,\eta }(G)$ has Lie algebra ${\mathfrak{sl}}_2$ of inner derivations and can be decomposed under spin: $H=H_…