Journal of Nonlinear Mathematical Physics

Volume 28, Issue 1, March 2021, Pages 123 - 133

Ideals Generated by Traces or by Supertraces in the Symplectic Reflection Algebra H1,V(I2(2m + 1)) II

Authors
I.A. Batalin, S.E. Konstein*, I.V. Tyutin
I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute, RAS 119991, Leninsky Prosp., 53, Moscow, Russia
*Corresponding author. Email: konstein@lpi.ru
Corresponding Author
S.E. Konstein
Received 21 August 2020, Accepted 24 August 2020, Available Online 10 December 2020.
DOI
https://doi.org/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 trν or the space of supertraces contains a degenerate nonzero supertrace strν 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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
28 - 1
Pages
123 - 133
Publication Date
2020/12
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.k.200922.012How to use a DOI?
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/).

Cite this article

TY  - JOUR
AU  - I.A. Batalin
AU  - S.E. Konstein
AU  - I.V. Tyutin
PY  - 2020
DA  - 2020/12
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  - https://doi.org/10.2991/jnmp.k.200922.012
ID  - Batalin2020
ER  -