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Supertraces on the Algebras of Observables of the Rational Calogero Model with Harmonic Potential | | S.E.Konstein
; M.A.Vasiliev
; | | Date: |
6 Dec 1995 | | Journal: | J.Math.Phys. 37 (1996) 2872-2891 | | Subject: | hep-th | | Affiliation: | P.N.Lebedev Physical Institute | | Abstract: | We define a complete set of supertraces on the algebra $SH_N(
u)$, the algebra of observables of the $N$-body rational Calogero model with harmonic interaction. This result extends the previously known results for the simplest cases of $N=1$ and $N=2$ to arbitrary $N$. It is shown that $SH_N(
u)$ admits $q(N)$ independent supertraces where $q(N)$ is a number of partitions of $N$ into a sum of odd positive integers, so that $q(N)>1$ for $Nge 3$. Some consequences of the existence of several independent supertraces of $SH_N (
u )$ are discussed such as the existence of ideals in associated $W_{infty}$ - type Lie superalgebras. | | Source: | arXiv, hep-th/9512038 | | Services: | Forum | Review | PDF | Favorites | |
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