Klein operator and the Number of independent Traces and Supertraces on the Superalgebra of Observables of Rational Calogero Model based on the Root System

DOI10.1080/14029251.2013.820410zbMath1420.37070arXiv1212.0508OpenAlexW2073522523MaRDI QIDQ5230896

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Publication date: 29 August 2019

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.0508

zbMATH Keywords

traceCalogero modelCherednik algebrasupertracealgebra of observables

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Applications of Lie algebras and superalgebras to integrable systems (17B80) ``Super (or ``skew) structure (16W55) Root systems (17B22)

Related Items (11)

Ideals generated by traces in the algebra of symplectic reflections \(H_{1,\nu_1,\nu_2}(I_2(2m))\) ⋮ The number of independent Traces and Supertraces on the Symplectic Reflection Algebra H_{1, η} (Γ ≀ S _N ) ⋮ Inverses of Cartan matrices of Lie algebras and Lie superalgebras ⋮ Double extensions of Lie superalgebras in characteristic 2 with nondegenerate invariant supersymmetric bilinear form ⋮ Non-degenerate invariant (super)symmetric bilinear forms on simple Lie (super)algebras ⋮ Traces on the Algebra of Observables of the Rational CalogeroModel Based on the Root System ⋮ Klein operator and the Number of independent Traces and Supertraces on the Superalgebra of Observables of Rational Calogero Model based on the Root System ⋮ The number of independent traces and supertraces on symplectic reflection algebras ⋮ Ideals generated by traces or by supertraces in the symplectic reflection algebra H_{1, ν} (I₂(2m + 1)) ⋮ 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

Cites Work

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• Supertraces on the algebras of observables of the rational Calogero models related to classical root systems
• Symplectic reflection algebras, Calogero-Moser space, and deformed Harish-Chandra homomorphism.
• Automorphisms of Coxeter groups of rank three
• The characters of the hecatonicosahedroidal group.
• Traces on the Algebra of Observables of the Rational CalogeroModel Based on the Root System
• Klein operator and the Number of independent Traces and Supertraces on the Superalgebra of Observables of Rational Calogero Model based on the Root System
• Supertraces on the algebras of observables of the rational Calogero model with harmonic potential
• Notes on Coxeter Transformations and the McKay Correspondence

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