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