Rational Calogero models based on rank-2 root systems: supertraces on the superalgebras of observables

TL;DR

This paper investigates the superalgebra of observables in rational Calogero models linked to rank-2 root systems, revealing the number of supertraces for specific models and highlighting new algebraic properties.

Contribution

It demonstrates the existence and count of supertraces in superalgebras of observables for Calogero models based on I_2(n) and G_2 root systems, providing new algebraic insights.

Findings

Superalgebra of I_2(n) models has [(n+1)/2] supertraces.

G_2 model's superalgebra has 3 independent supertraces.

Identifies algebraic structures specific to these Calogero models.

Abstract

It is shown that the superalgebra of observables of the rational Calogero model based on the root system of I_2(n) type possesses [(n+1)/2] supertraces. Model with three-particle interaction based on the root system G_2 belongs to this class of models and its superalgebra of observables has 3 independent supertraces.