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

Abstract

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: $H=H_0\oplus H_{1/2}\oplus H_1\oplus H_{3/2}\oplus ...$. We show that if the ideals ${\mathcal{I}}_i$ ($i=1,2$) of all the vectors from the kernel of degenerate bilinear forms $B_i(x,y):=s{p}_i(x\cdot y)$, where $s{p}_i$ are (super)traces on $H$, do exist, then ${\mathcal{I}}_1={\mathcal{I}}_2$ if and only if ${\mathcal{I}}_1\bigcap H_0={\mathcal{I}}_2\bigcap H_0$.

6 pages

References in corpus (1)

• Ideals generated by traces or by supertraces in the symplectic reflection algebra $H_{1,\nu }(I_2(2m+1))$

Cited by in corpus (2)

• Ideals generated by traces or by supertraces in the symplectic reflection algebra $H_{1,\nu }(I_2(2m+1))$ II
• Supertraces on queerified algebras