Traces on the Algebra of Observables of Rational Calogero Model based on the Root System

Abstract

It is shown that H_R(ν), the algebra of observables of the rational Calogero model based on the root system R, possesses T(R) independent traces, where T(R) is the number of conjugacy classes of elements without eigenvalue 1 belonging to the Coxeter group W(R) generated by the root system R. Simultaneously, we reproduced an older result: the algebra H_R(ν), considered as a superalgebra with a natural parity, possesses ST(R) independent supertraces, where ST(R) is the number of conjugacy classes of elements without eigenvalue -1 belonging to W(R).

Latex 2e, 25 pages

References in corpus (2)

• Klein operator and the Numbers of independent Traces and Supertraces on the Superalgebra of Observables of Rational Calogero Model based on the Root System
• Completions of symplectic reflection algebras

Cited by in corpus (5)

• Klein operator and the Numbers of independent Traces and Supertraces on the Superalgebra of Observables of Rational Calogero Model based on the Root System
• Hochschild cohomology of the Weyl algebra and Vasiliev's equations
• The number of independent Traces and Supertraces on Symplectic Reflection Algebras
• Connection between the ideals generated by traces and by supertraces in the superalgebras of observables of Calogero models
• Ideals generated by traces or by supertraces in the symplectic reflection algebra $H_{1,\nu }(I_2(2m+1))$