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
S.E. Konstein, I.V. Tyutin
Received 19 August 2019, Accepted 30 August 2019, Available Online 25 October 2019.
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If G is a finite Coxeter group, then symplectic reflection algebra H := H1,η (G) has Lie algebra 𝔰𝔩2 of inner derivations and can be decomposed under spin: H = H0 ⊕ H1/2 ⊕ H1 ⊕ H3/2 ⊕ ... 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 · y), where spi are (super)traces on H, do exist, then ℐ1 = ℐ2 if and only if ℐ1 ∩ H0 = ℐ2 ∩H0.
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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 - 10.1080/14029251.2020.1684005 ID - Konstein2019 ER -