Ideals Generated by Traces or by Supertraces in the Symplectic Reflection Algebra H_1,V(I₂(2m + 1)) II

DOI

10.2991/jnmp.k.200922.012How to use a DOI?

Keywords

symplectic reflection algebra; trace; supertrace; ideal; dihedral group

Abstract

The algebra 𝒣≔H1,ν(I2(2m+1)) of observables of the Calogero model based on the root system I₂(2m + 1) has an m-dimensional space of traces and an (m + 1)-dimensional space of supertraces. In the preceding paper we found all values of the parameter ν for which either the space of traces contains a degenerate nonzero trace tr_ν or the space of supertraces contains a degenerate nonzero supertrace str_ν and, as a consequence, the algebra 𝒣 has two-sided ideals: one consisting of all vectors in the kernel of the form Btrν(x,y)=trν(xy) or another consisting of all vectors in the kernel of the form Bstrν(x,y)=strν(xy) . We noticed that if ν=z2m+1 , where z∈𝕑\(2m+1)𝕑 , then there exist both a degenerate trace and a degenerate supertrace on 𝒣 . Here we prove that the ideals determined by these degenerate forms coincide.

Copyright

© 2020 The Authors. Published by Atlantis Press B.V.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)
View full text (HTML)

TY  - JOUR
AU  - I.A. Batalin
AU  - S.E. Konstein
AU  - I.V. Tyutin
PY  - 2020
DA  - 2020/12/10
TI  - Ideals Generated by Traces or by Supertraces in the Symplectic Reflection Algebra H₁,V(I₂(2m + 1)) II
JO  - Journal of Nonlinear Mathematical Physics
SP  - 123
EP  - 133
VL  - 28
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.k.200922.012
DO  - 10.2991/jnmp.k.200922.012
ID  - Batalin2020
ER  -