Volume 24, Issue 3, June 2017, Pages 405 - 425
Ideals generated by traces or by supertraces in the symplectic reflection algebra H1,ν (I2(2m + 1))
Authors
S.E. Konstein
I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute, Leninsky prosp. 53, Moscow 119991, Russia,konstein@lpi.ru
I.V. Tyutin
I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute, Leninsky prosp. 53, Moscow 119991, Russia,tyutin@lpi.ru
Received 6 January 2017, Accepted 10 May 2017, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2017.1341702How to use a DOI?
- Abstract
For each complex number ν, an associative symplectic reflection algebra ℋ := H1,ν (I2(2m + 1)), based on the group generated by root system I2(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 Bsp(x, y) = sp(xy) is degenerate. We find all values of the parameter ν 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 ℋ has a two-sided ideal of null-vectors. The analogous results for the case H1,ν1,ν2(I2(2m)) are also presented.
- Copyright
- © 2017 The Authors. Published by Atlantis Press and Taylor & Francis
- 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 - S.E. Konstein AU - I.V. Tyutin PY - 2021 DA - 2021/01/06 TI - Ideals generated by traces or by supertraces in the symplectic reflection algebra H₁,ν (I₂(2m + 1)) JO - Journal of Nonlinear Mathematical Physics SP - 405 EP - 425 VL - 24 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2017.1341702 DO - 10.1080/14029251.2017.1341702 ID - Konstein2021 ER -