Ideals Generated by Traces or by Supertraces in the Symplectic Reflection Algebra H1,V(I2(2m + 1)) II
- 10.2991/jnmp.k.200922.012How to use a DOI?
- symplectic reflection algebra; trace; supertrace; ideal; dihedral group
The algebra 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 or another consisting of all vectors in the kernel of the form . We noticed that if , where , then there exist both a degenerate trace and a degenerate supertrace on . Here we prove that the ideals determined by these degenerate forms coincide.
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Cite this article
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 -