Supertraces on the Algebras of Observables of the Rational Calogero Model with Harmonic Potential

Details Supertraces on the Algebras of Observables of the Rational Calogero Model with Harmonic Potential Supertraces on the Algebras of Observables of the Rational Calogero Model with Harmonic Potential

1995-12-06

arxiv.org/abs/hep-th/9512038v1

J.Math.Phys. 37 (1996) 2872-2891

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, LATEX

Scientific paper

10.1063/1.531544

We define a complete set of supertraces on the algebra $SH_N(\nu)$, 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 $SH_N(\nu)$ 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 $N\ge 3$. Some consequences of the existence of several independent supertraces of $SH_N (\nu )$ are discussed such as the existence of ideals in associated $W_{\infty}$ - type Lie superalgebras.

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