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

Abstract

For each complex number $\nu$, an associative symplectic reflection algebra $\mathcal{H}:=H_{1,\nu }(I_2(2m+1))$, based on the group generated by root system $I_2(2m+1)$, has an $m$-dimensional space of traces and an $(m+1)$-dimensional space of supertraces. A (super)trace $sp$ is said to be degenerate if the corresponding bilinear (super)symmetric form $B_{sp}(x,y)=sp(xy)$ is degenerate. We find all values of the parameter $\nu$ for which either the space of traces contains a degenerate nonzero trace or the space of supertraces contains a degenerate nonzero supertrace and, as a consequence, the algebra $\mathcal{H}$ has a two-sided ideal of null-vectors. The analogous results for the algebra $H_{1,{\nu }_1,{\nu }_2}(I_2(2m))$ are also presented.

20 pages, LaTeX 2e

Cited by in corpus (1)

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