Compactness property of Lie polynomials in the creation and annihilation operators of the \(q\)-oscillator

DOI10.1007/s11005-020-01304-xzbMath1468.17015OpenAlexW3037133551MaRDI QIDQ2224486

Rafael Reno S. Cantuba

Publication date: 3 February 2021

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11005-020-01304-x

zbMATH Keywords

Lie algebraFredholm operatorcompact operatorcreation operatorcommutation relationannihilation operatorcommutatorLaurent polynomialCalkin algebracommutator algebra\(q\)-oscillatorunilateral weighted shift\(q\)-deformed Heisenberg algebraLie polynomial

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Representations of Lie algebras and Lie superalgebras, analytic theory (17B15)

Related Items

Lie polynomials in an algebra defined by a linearly twisted commutation relation ⋮ Lie structure of the Heisenberg-Weyl algebra ⋮ A CASIMIR ELEMENT INEXPRESSIBLE AS A LIE POLYNOMIAL

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