Journal of Nonlinear Mathematical Physics

Volume 27, Issue 1, October 2019, Pages 7 - 11

Connection between the ideals generated by traces and by supertraces in the superalgebras of observables of Calogero models

Authors
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, konstein@lpi.ru, tyutin@lpi.ru
*Corresponding author
Corresponding Author
S.E. Konstein
Received 19 August 2019, Accepted 30 August 2019, Available Online 25 October 2019.
DOI
https://doi.org/10.1080/14029251.2020.1684005How to use a DOI?
Abstract

If G is a finite Coxeter group, then symplectic reflection algebra H := H1,Ξ· (G) has Lie algebra 𝔰𝔩2 of inner derivations and can be decomposed under spin: H = H0 βŠ• H1/2 βŠ• H1 βŠ• H3/2 βŠ• ... We show that if the ideals ℐi (i = 1,2) of all the vectors from the kernel of degenerate bilinear forms Bi(x,y) := spi(x Β· y), where spi are (super)traces on H, do exist, then ℐ1 = ℐ2 if and only if ℐ1 ∩ H0 = ℐ2 ∩H0.

Copyright
Β© 2020 The Authors. Published by Atlantis 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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 1
Pages
7 - 11
Publication Date
2019/10/25
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2020.1684005How to use a DOI?
Copyright
Β© 2020 The Authors. Published by Atlantis 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  - 2019
DA  - 2019/10/25
TI  - Connection between the ideals generated by traces and by supertraces in the superalgebras of observables of Calogero models
JO  - Journal of Nonlinear Mathematical Physics
SP  - 7
EP  - 11
VL  - 27
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1684005
DO  - https://doi.org/10.1080/14029251.2020.1684005
ID  - Konstein2019
ER  -